Electrochromic multi-layer devices with current modulating structure

ABSTRACT

A multi-layer device comprising a first substrate, a first electrically conductive layer on a surface thereof, and a first current modulating layer, the first electrically conductive layer having a sheet resistance to the flow of electrical current through the first electrically conductive layer that varies as a function of position.

FIELD OF THE INVENTION

The present invention generally relates to switchable electrochromicdevices, such as architectural windows, capable of coordinated switchingover substantially their entire area or a selected subregion of theirentire area. More particularly, and in one preferred embodiment, thepresent invention is directed to switchable electrochromic multi-layerdevices, particularly large area rectangular windows for architecturalapplications that switch in a spatially coordinated manner oversubstantially their entire area or a selected subregion of their entirearea; optionally these are of non-uniform shape, optionally they switchsynchronously, i.e., uniformly, over substantially their entire area ora selected subregion of their entire area, or in a coordinated butnonsynchronous manner (e.g., from side-to-side, or top-to-bottom) from afirst optical state, e.g., a transparent state, to a second opticalstate, e.g., a reflective or colored state.

BACKGROUND OF THE INVENTION

Commercial switchable glazing devices are well known for use as mirrorsin motor vehicles, automotive windows, aircraft window assemblies,sunroofs, skylights, architectural windows. Such devices may comprise,for example, inorganic electrochromic devices, organic electrochromicdevices, switchable mirrors, and hybrids of these having two conductinglayers with one or more active layers between the conducting layers.When a voltage is applied across these conducting layers the opticalproperties of a layer or layers in between change. Such optical propertychanges are typically a modulation of the transmissivity of the visibleor the solar subportion of the electromagnetic spectrum. Forconvenience, the two optical states will be referred to as a lightenedstate and a darkened state in the following discussion, but it should beunderstood that these are merely examples and relative terms (i.e., oneof the two states is “lighter” or more transmissive than the otherstate) and that there could be a set of lightened and darkened statesbetween the extremes that are attainable for a specific electrochromicdevice; for example, it is feasible to switch between intermediatelightened and darkened states in such a set.

Switching between a lightened and a darkened state in relatively smallelectrochromic devices such as an electrochromic rear-view mirrorassembly is typically quick and uniform, whereas switching between thelightened and darkened state in a large area electrochromic device canbe slow and spatially non-uniform. Gradual, non-uniform coloring orswitching is a common problem associated with large area electrochromicdevices. This problem, commonly referred to as the “iris effect,” istypically the result of the voltage drop through the transparentconductive coatings providing electrical contact to one side or bothsides of the device. For example, when a voltage is initially applied tothe device, the potential is typically the greatest in the vicinity ofthe edge of the device (where the voltage is applied) and the least atthe center of the device; as a result, there may be a significantdifference between the transmissivity near the edge of the device andthe transmissivity at the center of the device. Over time, however, thedifference in applied voltage between the center and edge decreases and,as a result, the difference in transmissivity at the center and edge ofthe device decreases. In such circumstances, the electrochromic mediumwill typically display non-uniform transmissivity by initially changingthe transmissivity of the device in the vicinity of the appliedpotential, with the transmissivity gradually and progressively changingtowards the center of the device as the switching progresses. While theiris effect is most commonly observed in relatively large devices, italso can be present in smaller devices that have correspondingly higherresistivity conducting layers.

SUMMARY OF THE INVENTION

Among the various aspects of the present invention is the provision ofrelatively large-area electrochromic multi-layer devices capable ofcoordinated switching and coloring, across substantially its entire areathat can be easily manufactured.

Briefly, therefore, the present invention is directed to a multi-layerdevice comprising a first substrate and a layered stack that istransmissive to electromagnetic radiation having a wavelength in therange of infrared to ultraviolet on a surface of the first substrate,the layered stack comprising a first electrically conductive layerhaving an upper surface and a lower surface, and a current modulatingstructure, the electrically conductive layer and the current modulatingstructure each covering at least 0.01 m² of the surface of the firstsubstrate, the lower surface of the first electrically conductive layerbeing on the surface of the first substrate, the current modulatingstructure being on the upper surface of the first electricallyconductive layer, the current modulating structure comprising a materialhaving a resistivity of at least 10⁴ ohm-cm, the first electricallyconductive layer having a sheet resistance, R_(s), to the flow ofelectrical current through the first electrically conductive layer thatvaries as a function of position in the first electrically conductivelayer, wherein an average sheet resistance in a first region of thefirst electrically conductive layer circumscribed by a first convexpolygon to the average sheet resistance in a second region of the firstelectrically conductive layer circumscribed by a second convex polygonis at least 2, the first and second regions circumscribed by the firstand second convex polygons, respectively, each comprising at least 25%of the surface area of the first electrically conductive layer.

Another aspect of the present invention is an electrochromic devicecomprising a first substrate, a first electrically conductive layer, afirst current modulating structure, a first electrode layer, a secondelectrically conductive layer and a second substrate, the electricallyconductive layer and the current modulating structure each covering atleast 0.01 m² of the surface of the first substrate, the currentmodulating structure being between the first electrically conductivelayer and the first electrode layer, the first current modulatingstructure comprising a material having a resistivity of at least 10⁴ohm-cm, the first electrically conductive layer having a sheetresistance, R_(s), to the flow of electrical current through the firstelectrically conductive layer that varies as a function of position inthe first electrically conductive layer, wherein an average sheetresistance in a first region of the first electrically conductive layercircumscribed by a first convex polygon to the average sheet resistancein a second region of the first electrically conductive layercircumscribed by a second convex polygon is at least 2, the first andsecond regions circumscribed by the first and second convex polygons,respectively, each comprising at least 25% of the surface area of thefirst electrically conductive layer.

Another aspect of the present invention is a process for the preparationof a multi-layer device comprising forming a multi-layer layer structurecomprising an electrochromic layer between and in electrical contactwith a first and a second electrically conductive layer, and a firstcurrent modulating structure between the first electrically conductivelayer and the electrochromic layer, the first current modulatingstructure comprising a material having a resistivity of at least 10⁴ohm-cm, the first and/or the second electrically conductive layer havinga spatially varying sheet resistance, R_(s), to the flow of electricalcurrent through the first and/or the second electrically conductivelayer that varies as a function of position in the first and/or thesecond electrically conductive layer, respectively, wherein the ratio ofthe average sheet resistance in a first region of the first electricallyconductive layer circumscribed by a first convex polygon to the averagesheet resistance in a second region of the first electrically conductivelayer circumscribed by a second convex polygon is at least 2, the firstand second regions circumscribed by the first and second convexpolygons, respectively, each comprising at least 25% of the surface areaof the first electrically conductive layer.

Other objects and features will be in part apparent and in part pointedout hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic cross-section of a multi-layer electrochromicdevice of the present invention.

FIG. 2A-2E is a series of contour maps of the sheet resistance, R_(s),in the first and/or second electrically conductive layer as a functionof position (two-dimensional) within the first and/or secondelectrically conductive layer showing isoresistance lines (alsosometimes referred to as contour lines) and resistance gradient lines(lines perpendicular to the isoresistance lines) resulting from variousalternative arrangements of bus bars for devices having square andcircular perimeters.

FIG. 3 is an exploded view of the multi-layer device of FIG. 1.

FIGS. 4A and 4B are schematic cross-sections showing two embodiments ofthe present invention in which the cross-layer resistance of a currentmodulating structure is varied as a function of position by patterning alayer of resistive material with a layer of insulating material. FIGS.4C and 4D are corresponding exemplary patterns of resistive andinsulating material layers.

FIGS. 5A and 5B are schematic cross-sections showing two embodiments ofthe present invention in which the cross-layer resistance of a currentmodulating structure is varied as a function of position by patterning alayer of resistive material with a layer of insulating material. FIGS.5C and 5D are corresponding exemplary patterns of resistive andinsulating material layers.

FIGS. 6A and 6B are schematic cross-sections showing two embodiments ofthe present invention in which the cross-layer resistance of a currentmodulating structure is varied as a function of position by patterning alayer of resistive material with a layer of insulating material. FIG. 6Cis an exemplary pattern of resistive and insulating material layers.

FIGS. 7A and 7B are schematic cross-sections showing two embodiments ofthe present invention in which the cross-layer resistance of a currentmodulating structure is varied as a function of position by patterning alayer of resistive material with a layer of insulating material. FIG. 7Cis an exemplary pattern of resistive and insulating material layers.

FIGS. 8A and 8B are schematic cross-sections showing two embodiments ofthe present invention in which the cross-layer resistance of a currentmodulating structure is varied as a function of position by patterning alayer of resistive material with a layer of insulating material. FIG. 8Cis an exemplary pattern of resistive and insulating material layers.

FIGS. 9A and 9B are schematic cross-sections showing two embodiments ofthe present invention in which the cross-layer resistance of a currentmodulating structure is varied as a function of position by patterning alayer of resistive material with a layer of insulating material. FIG. 9Cis an exemplary pattern of resistive and insulating material layers.

FIGS. 10A-10E show contour maps of the cross-layer resistance, R_(C), ina current modulating structure of the present invention.

FIG. 11 is an exploded view of the multi-layer device of FIG. 1.

FIG. 12 is a schematic cross-section of an alternative embodiment of theelectrochromic device of the present invention.

FIG. 13 is a schematic cross-section of an alternative embodiment of theelectrochromic device of the present invention.

FIG. 14 is a schematic cross-section of an alternative embodiment of theelectrochromic device of the present invention.

FIG. 15 shows two line graphs depicting insulator fill factors as afunction of position (cm).

FIG. 16 is a line graph depicting resistor layer thickness (nm) as afunction of position (cm).

FIG. 17 is a schematic cross-section of an alternative embodiment of amulti-layer electrochromic device of the present invention.

FIG. 18 is a schematic cross-section of an alternative embodiment of amulti-layer electrochromic device of the present invention.

FIG. 19 is a 1-D lumped element circuit model diagram used to simulatedynamic behavior of an electrochromic device of the present invention.

Corresponding reference characters indicate corresponding partsthroughout the drawings. Additionally, relative thicknesses of thelayers in the different figures do not represent the true relationshipin dimensions. For example, the substrates are typically much thickerthan the other layers. The figures are drawn only for the purpose toillustrate connection principles, not to give any dimensionalinformation.

ABBREVIATIONS AND DEFINITIONS

The following definitions and methods are provided to better define thepresent invention and to guide those of ordinary skill in the art in thepractice of the present invention. Unless otherwise noted, terms are tobe understood according to conventional usage by those of ordinary skillin the relevant art.

The term “anodic electrochromic layer” refers to an electrode layer thatchanges from a more transmissive state to a less transmissive state uponthe removal of ions.

The term “cathodic electrochromic layer” refers to an electrode layerthat changes from a more transmissive state to a less transmissive stateupon the insertion of ions.

The terms “conductive” and “resistive” refer to the electricalconductivity and electrical resistivity of a material.

The term “convex polygon” refer to a simple polygon in which everyinternal angle is less than or equal to 180 degrees, and every linesegment between two vertices remains inside or on the boundary of thepolygon. Exemplary convex polygons include triangles, rectangles,pentagons, hexagons, etc., in which every internal angle is less than orequal to 180 degrees and every line segment between two vertices remainsinside or on the boundary of the polygon.

The term “cross-layer resistance” as used in connection with a layer (orelongate structure) is the resistance to current flow substantiallynormal to a major surface of the layer (or elongate structure).

The term “electrochromic layer” refers to a layer comprising anelectrochromic material.

The term “electrochromic material” refers to materials that are able tochange their optical properties, reversibly, as a result of theinsertion or extraction of ions and electrons. For example, anelectrochromic material may change between a colored, translucent stateand a transparent state.

The term “electrode layer” refers to a layer capable of conducting ionsas well as electrons. The electrode layer contains a species that can beoxidized when ions are inserted into the material and contains a speciesthat can be reduced when ions are extracted from the layer. This changein oxidation state of a species in the electrode layer is responsiblefor the change in optical properties in the device.

The term “electrical potential,” or simply “potential,” refers to thevoltage occurring across a device comprising an electrode/ionconductor/electrode stack.

The term “sheet resistance” as used in connection with a layer (or anelongate structure) is the resistance to current flow substantiallyparallel to a major surface of the layer (or the elongate structure).

The term “transmissive” is used to denote transmission ofelectromagnetic radiation through a material.

The term “transparent” is used to denote substantial transmission ofelectromagnetic radiation through a material such that, for example,bodies situated beyond or behind the material can be distinctly seen orimaged using appropriate image sensing technology.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 depicts a cross-sectional structural diagram of electrochromicdevice 1 according to a first embodiment of the present invention.Moving outward from the center, electrochromic device 1 comprises an ionconductor layer 10. First electrode layer 20 is on one side of and incontact with a first surface of ion conductor layer 10, and secondelectrode layer 21 is on the other side of and in contact with a secondsurface of ion conductor layer 10. In addition, at least one of firstand second electrode layers 20, 21 comprises electrochromic material; inone embodiment, first and second electrode layers 20, 21 each compriseelectrochromic material. The central structure, that is, layers 20, 10,21, is positioned between first and second current modulating structures30 and 31. First and second current modulating structures 30 and 31, inturn, are adjacent first and second electrically conductive layers 22and 23, respectively, which are arranged against outer substrates 24,25, respectively. Elements 22, 30, 20, 10, 21, 31 and 23 arecollectively referred to as an electrochromic stack 28.

Electrically conductive layer 22 is in electrical contact with oneterminal of a power supply (not shown) via bus bar 26 and electricallyconductive layer 23 is in electrical contact with the other terminal ofa power supply (not shown) via bus bar 27 whereby the transmissivity ofelectrochromic device 10 may be changed by applying a voltage pulse toelectrically conductive layers 22 and 23. The pulse causes electrons andions to move between first and second electrode layers 20 and 21 and, asa result, electrochromic material in the first and/or second electrodelayer(s) change(s) optical states, thereby switching electrochromicdevice 1 from a more transmissive state to a less transmissive state, orfrom a less transmissive state to a more transmissive state. In oneembodiment, electrochromic device 1 is transparent before the voltagepulse and less transmissive (e.g., more reflective or colored) after thevoltage pulse or vice versa.

It should be understood that the reference to a transition between aless transmissive and a more transmissive state is non-limiting and isintended to describe the entire range of transitions attainable byelectrochromic materials to the transmissivity of electromagneticradiation. For example, the change in transmissivity may be a changefrom a first optical state to a second optical state that is (i)relatively more absorptive (i.e., less transmissive) than the firststate, (ii) relatively less absorptive (i.e., more transmissive) thanthe first state, (iii) relatively more reflective (i.e., lesstransmissive) than the first state, (iv) relatively less reflective(i.e., more transmissive) than the first state, (v) relatively morereflective and more absorptive (i.e., less transmissive) than the firststate or (vi) relatively less reflective and less absorptive (i.e., moretransmissive) than the first state. Additionally, the change may bebetween the two extreme optical states attainable by an electrochromicdevice, e.g., between a first transparent state and a second state, thesecond state being opaque or reflective (mirror). Alternatively, thechange may be between two optical states, at least one of which isintermediate along the spectrum between the two extreme states (e.g.,transparent and opaque or transparent and mirror) attainable for aspecific electrochromic device. Unless otherwise specified herein,whenever reference is made to a less transmissive and a moretransmissive, or even a bleached-colored transition, the correspondingdevice or process encompasses other optical state transitions such asnon-reflective-reflective, transparent-opaque, etc. Further, the term“bleached” refers to an optically neutral state, e.g., uncolored,transparent or translucent. Still further, unless specified otherwiseherein, the “color” of an electrochromic transition is not limited toany particular wavelength or range of wavelengths. As understood bythose of skill in the art, the choice of appropriate electrochromic andcounter electrode materials governs the relevant optical transition.

In general, the change in transmissivity preferably comprises a changein transmissivity to electromagnetic radiation having a wavelength inthe range of infrared to ultraviolet radiation. For example, in oneembodiment the change in transmissivity is predominately a change intransmissivity to electromagnetic radiation in the infrared spectrum. Ina second embodiment, the change in transmissivity is to electromagneticradiation having wavelengths predominately in the visible spectrum. In athird embodiment, the change in transmissivity is to electromagneticradiation having wavelengths predominately in the ultraviolet spectrum.In a fourth embodiment, the change in transmissivity is toelectromagnetic radiation having wavelengths predominately in theultraviolet and visible spectra. In a fifth embodiment, the change intransmissivity is to electromagnetic radiation having wavelengthspredominately in the infrared and visible spectra. In a sixthembodiment, the change in transmissivity is to electromagnetic radiationhaving wavelengths predominately in the ultraviolet, visible andinfrared spectra.

The materials making up electrochromic stack 28 may comprise organic orinorganic materials, and they may be solid or liquid. For example, incertain embodiments the electrochromic stack 28 comprises materials thatare inorganic, solid (i.e., in the solid state), or both inorganic andsolid. Inorganic materials have shown better reliability inarchitectural applications. Materials in the solid state can also offerthe advantage of not having containment and leakage issues, as materialsin the liquid state often do. It should be understood that any one ormore of the layers in the stack may contain some amount of organicmaterial, but in many implementations one or more of the layers containslittle or no organic matter. The same can be said for liquids that maybe present in one or more layers in small amounts. In certain otherembodiments some or all of the materials making up electrochromic stack28 are organic. Organic ion conductors can offer higher mobilities andthus potentially better device switching performance. Organicelectrochromic layers can provide higher contrast ratios and morediverse color options. Each of the layers in the electrochromic deviceis discussed in detail, below. It should also be understood that solidstate material may be deposited or otherwise formed by processesemploying liquid components such as certain processes employing sol-gelsor chemical vapor deposition.

Referring again to FIG. 1, the power supply (not shown) connected to busbars 26, 27 is typically a voltage source with optional current limitsor current control features and may be configured to operate inconjunction with local thermal, photosensitive or other environmentalsensors. The voltage source may also be configured to interface with anenergy management system, such as a computer system that controls theelectrochromic device according to factors such as the time of year,time of day, and measured environmental conditions. Such an energymanagement system, in conjunction with large area electrochromic devices(e.g., an electrochromic architectural window), can dramatically lowerthe energy consumption of a building.

At least one of the substrates 24, 25 is preferably transparent, inorder to reveal the electrochromic properties of the stack 28 to thesurroundings. Any material having suitable optical, electrical, thermal,and mechanical properties may be used as first substrate 24 or secondsubstrate 25. Such substrates include, for example, glass, plastic,metal, and metal coated glass or plastic. Non-exclusive examples ofpossible plastic substrates are polycarbonates, polyacrylics,polyurethanes, urethane carbonate copolymers, polysulfones, polyimides,polyacrylates, polyethers, polyester, polyethylenes, polyalkenes,polyimides, polysulfides, polyvinylacetates and cellulose-basedpolymers. If a plastic substrate is used, it may be barrier protectedand abrasion protected using a hard coat of, for example, a diamond-likeprotection coating, a silica/silicone anti-abrasion coating, or thelike, such as is well known in the plastic glazing art. Suitable glassesinclude either clear or tinted soda lime glass, including soda limefloat glass. The glass may be tempered or untempered. In someembodiments of electrochromic device 1 with glass, e.g. soda lime glass,used as first substrate 24 and/or second substrate 25, there is a sodiumdiffusion barrier layer (not shown) between first substrate 24 and firstelectrically conductive layer 22 and/or between second substrate 25 andsecond electrically conductive layer 23 to prevent the diffusion ofsodium ions from the glass into first and/or second electricallyconductive layer 23. In some embodiments, second substrate 25 isomitted.

In one preferred embodiment of the invention, first substrate 24 andsecond substrate 25 are each float glass. In certain embodiments forarchitectural applications, this glass is at least 0.5 meters by 0.5meters, and can be much larger, e.g., as large as about 3 meters by 4meters. In such applications, this glass is typically at least about 2mm thick and more commonly 4-6 mm thick.

Independent of application, the electrochromic devices of the presentinvention may have a wide range of sizes. In general, it is preferredthat the electrochromic device comprise a substrate having a surfacewith a surface area of at least 0.01 meter². For example, in certainembodiments, the electrochromic device comprises a substrate having asurface with a surface area of at least 0.1 meter². By way of furtherexample, in certain embodiments, the electrochromic device comprises asubstrate having a surface with a surface area of at least 1 meter². Byway of further example, in certain embodiments, the electrochromicdevice comprises a substrate having a surface with a surface area of atleast 5 meter². By way of further example, in certain embodiments, theelectrochromic device comprises a substrate having a surface with asurface area of at least 10 meter².

At least one of the two electrically conductive layers 22, 23 is alsopreferably transparent in order to reveal the electrochromic propertiesof the stack 28 to the surroundings. In one embodiment, electricallyconductive layer 23 is transparent. In another embodiment, electricallyconductive layer 22 is transparent. In another embodiment, electricallyconductive layers 22, 23 are each transparent. In certain embodiments,one or both of the electrically conductive layers 22, 23 is inorganicand/or solid. Electrically conductive layers 22 and 23 may be made froma number of different transparent materials, including transparentconductive oxides, thin metallic coatings, networks of conductive nanoparticles (e.g., rods, tubes, dots) conductive metal nitrides, andcomposite conductors. Transparent conductive oxides include metal oxidesand metal oxides doped with one or more metals. Examples of such metaloxides and doped metal oxides include indium oxide, indium tin oxide,doped indium oxide, tin oxide, doped tin oxide, zinc oxide, aluminumzinc oxide, doped zinc oxide, ruthenium oxide, doped ruthenium oxide andthe like. Transparent conductive oxides are sometimes referred to as(TCO) layers. Thin metallic coatings that are substantially transparentmay also be used. Examples of metals used for such thin metalliccoatings include gold, platinum, silver, aluminum, nickel, and alloys ofthese. Examples of transparent conductive nitrides include titaniumnitrides, tantalum nitrides, titanium oxynitrides, and tantalumoxynitrides. Electrically conducting layers 22 and 23 may also betransparent composite conductors. Such composite conductors may befabricated by placing highly conductive ceramic and metal wires orconductive layer patterns on one of the faces of the substrate and thenover-coating with transparent conductive materials such as doped tinoxides or indium tin oxide. Ideally, such wires should be thin enough asto be invisible to the naked eye (e.g., about 100 pm or thinner).Non-exclusive examples of electron conductors 22 and 23 transparent tovisible light are thin films of indium tin oxide (ITO), tin oxide, zincoxide, titanium oxide, n- or p-doped zinc oxide and zinc oxyfluoride.Metal-based layers, such as ZnS/Ag/ZnS and carbon nanotube layers havebeen recently explored as well. Depending on the particular application,one or both electrically conductive layers 22 and 23 may be made of orinclude a metal grid.

To facilitate more rapid switching of electrochromic device 1 from astate of relatively greater transmittance to a state of relativelylesser transmittance, or vice versa, at least one of electricallyconductive layers 22, 23 preferably has a sheet resistance, R_(s), tothe flow of electrons through the layer that is non-uniform. Forexample, in one embodiment at least one of first and second electricallyconductive layers 22, 23 has a non-uniform sheet resistance to the flowof electrons through the layer and has a graded thickness orcomposition, or comprises a patterned composite layer. By way of furtherexample, in one embodiment one of first and second electricallyconductive layers 22, 23 comprises a graded thickness, a gradedcomposition or a patterned composite layer having a non-uniform sheetresistance to the flow of electrons through the layer and and the otherhas a uniform sheet resistance to the flow of electrons through thelayer. By way of further example, in one embodiment one of first andsecond electrically conductive layers 22, 23 comprises one of first andsecond electrically conductive layers 22, 23 comprises a gradedthickness, a graded composition or a patterned composite layer having anon-uniform sheet resistance to the flow of electrons through the layerand the other also has a non-uniform sheet resistance to the flow ofelectrons through the layer. Without being bound by any particulartheory, it is presently believed that an effective variation in thesheet resistance of electrically conductive layer 22, electricallyconductive layer 23, or electrically conductive layer 22 andelectrically conductive layer 23 may further improve the switchingperformance of the device by controlling the voltage drop in theconductive layer to provide uniform potential drop or a desirednon-uniform potential drop across the device over an area of the deviceat least 25% of the device area.

In one embodiment, one of electrically conductive layers 22, 23 is acomposite of a first material, an electrically conductive material, anda second less conductive material. For example, in one embodiment thefirst material has a resistivity of less than about 10²Ω·cm and thesecond material has a resistivity that is greater than the resistivityof the first material by a factor of at least 10². By way of furtherexample, in one embodiment the first material has a resistivity of lessthan about 10²Ω·cm and the second material has a resistivity that isgreater than the resistivity of the first material by a factor of atleast 10³. By way of further example, in one embodiment the firstmaterial has a resistivity of less than about 10²Ω·cm and the secondmaterial has a resistivity that is greater than the resistivity of thefirst material by a factor of at least 10⁴. By way of further example,in one embodiment the first material has a resistivity of less thanabout 10²Ω·cm and the second material has a resistivity that is greaterthan the resistivity of the first material by a factor of at least 10⁵.By way of further example, in one embodiment the first material has aresistivity of less than about 10²Ω·cm and the second material has aresistivity that is greater than the resistivity of the first materialby a factor of at least 10⁶. By way of further example, in oneembodiment the first material has a resistivity of less than about10²Ω·cm and the second material has a resistivity that is greater thanthe resistivity of the first material by a factor of at least 10⁷. Byway of further example, in one embodiment the first material has aresistivity of less than about 10²Ω·cm and the second material has aresistivity that is greater than the resistivity of the first materialby a factor of at least 10⁸. By way of further example, in each of theforegoing embodiments, the first and/or second material is transparent.In one such exemplary embodiment, the first material may be selectedfrom transparent conductive oxides, thin metallic coatings, networks ofconductive nano particles (e.g., rods, tubes, dots) conductive metalnitrides, and composite conductors and the second material may beselected, in one embodiment, from materials having a resistivity of atleast 10⁴Ω·cm and, in another embodiment, from materials having aresistivity of at least 10¹⁰Ω·cm.

In a further exemplary embodiment where electrically conductive layers22, 23 is a composite of a first material, an electrically conductivematerial, and a second less conductive material, the first material hasa sheet resistance Rs of less than about 20 Ω/□ and the second materialhas a resistivity and thickness such that it has a sheet resistance thatis greater than the sheet resistance of the first material by a factorof at least 5. By way of further example, in one embodiment the firstmaterial has a sheet resistance Rs less than about 20 Ω/□ and the secondmaterial has a resistivity and thickness such that it has a sheetresistance that is greater than the sheet resistance of the firstmaterial by a factor of at least 10. By way of further example, in oneembodiment the first material has a sheet resistance Rs of less thanabout 20 Ω/□ and the second material has a resistivity and thicknesssuch that it has a sheet resistance that is greater than the sheetresistance of the first material by a factor of at least 15. By way offurther example, in one embodiment the first material has a sheetresistance Rs of around 15 Ω/□ and the second material has a resistivityand thickness such that it has a sheet resistance that is greater thanthe sheet resistance of the first material by a factor of at least 20.By way of further example, in one embodiment the first material has asheet resistance Rs of around 15 Ω/□ and the second material has aresistivity and thickness such that it has a sheet resistance that isgreater than the sheet resistance of the first material by a factor ofat least 30. By way of further example, in each of the foregoingembodiments, the first and/or second material is transparent. In onesuch exemplary embodiment, the first material may be selected fromtransparent conductive oxides, thin metallic coatings, networks ofconductive nano particles (e.g., rods, tubes, dots) conductive metalnitrides, and composite conductors and the second material may beselected, in one embodiment, from materials having a resistivity of atleast 10⁻⁵Ω·cm and, in another embodiment, from materials having aresistivity of at least 10⁵Ω·cm.

In general, the second, less conductive, material comprised by apatterned electrically conductive layer of the present invention may beany material exhibiting sufficient resistivity, optical transparency,and chemical stability for the intended application. For example, insome embodiments, at least one of electrically conductive layers 22, 23comprise a resistive or insulating material with high chemicalstability.. By way of further example, in some embodiments at least oneof electrically conductive layers 22, 23 comprise an insulator materialselected from the group consisting of alumina, silica, porous silica,fluorine doped silica, carbon doped silica, silicon nitride, siliconoxynitride, hafnia, magnesium fluoride, magnesium oxide, poly(methylmethacrylate) (PMMA), polyimides, polymeric dielectrics such aspolytetrafluoroethylene (PTFE), silicones, and combinations thereof.Exemplary resistive materials include zinc oxide, zinc sulfide, titaniumoxide, and gallium (III) oxide, yttrium oxide, zirconium oxide, aluminumoxide, indium oxide, stannic oxide and germanium oxide. In oneembodiment, one or both of first and electrically conductive layers 22,23 comprise(s) one or more of such resistive materials. In anotherembodiment, one or both of first and electrically conductive layers 22,23 comprise(s) one or more of such insulating materials. In anotherembodiment, one or both of first and second electrically conductivelayers 22, 23 comprise(s) one or more of such resistive materials andone or more of such insulating materials.

Depending upon the application, the relative proportions of the firstmaterial, i.e., the material having a resistivity of less than about10²Ω·cm (and preferably transparent), and the second material, i.e., thematerial having a resistivity that exceeds the resistivity of the firstmaterial by a factor of at least 10² may vary substantially inelectrically conductive layer 22, electrically conductive layer 23, orin each of electrically conductive layers 22, 23. In general, however,the second material constitutes at least about 5 vol % of at least oneof electrically conductive layers 22, 23. For example, in one embodimentthe second material constitutes at least about 10 vol % of at least oneof electrically conductive layers 22, 23. By way of further example, inone embodiment the second material constitutes at least about 20 vol %of at least one of electrically conductive layers 22, 23. By way offurther example, in one embodiment the second material constitutes atleast about 30 vol % of at least one of electrically conductive layers22, 23. By way of further example, in one embodiment the second materialconstitutes at least about 40 vol % of at least one of electricallyconductive layers 22, 23. In general, however, the second material willtypically not constitute more than about 70 vol % of either ofelectrically conductive layers 22, 23.

The thickness of the electrically conductive layer may be influenced bythe composition of the material comprised within the layer and itstransparent character. In some embodiments, electrically conductivelayers 22 and 23 are transparent and each have a thickness that isbetween about 1000 nm and about 50 nm. In some embodiments, thethickness of electrically conductive layers 22 and 23 is between about500 nm and about 100 nm. In other embodiments, the electricallyconductive layers 22 and 23 each have a thickness that is between about400 nm and about 200 nm. In general, thicker or thinner layers may beemployed so long as they provide the necessary electrical properties(e.g., conductivity) and optical properties (e.g., transmittance). Forcertain applications it will generally be preferred that electricallyconductive layers 22 and 23 be as thin as possible to increasetransparency and to reduce cost.

Referring again to FIG. 1, the function of the electrically conductivelayers is to apply the electric potential provided by a power supplyover the entire surface of the electrochromic stack 28 to interiorregions of the stack. The electric potential is transferred to theconductive layers though electrical connections to the conductivelayers. In some embodiments, bus bars, one in contact with firstelectrically conductive layer 22 and one in contact with secondelectrically conductive layer 23 provide the electric connection betweenthe voltage source and the electrically conductive layers 22 and 23.

In one embodiment, the sheet resistance, R_(s), of the first and secondelectrically conductive layers 22 and 23 is about 500 Ω/□ to 1 Ω/□. Insome embodiments, the sheet resistance of first and second electricallyconductive layers 22 and 23 is about 100 Ω/□ to 5 Ω/□.

To facilitate more rapid switching of electrochromic device 1 from astate of relatively greater transmittance to a state of relativelylesser transmittance, or vice versa, at least one of electricallyconductive layers 22, 23 comprises a sheet resistance, R_(s), to theflow of electrons through the layer that is non-uniform. For example, inone embodiment only one of first and second electrically conductivelayers 22, 23 comprises a non-uniform sheet resistance to the flow ofelectrons through the layer and the other has a uniform or non-uniformsheet resistance to the flow of electrons through the layer. By way offurther example, in one embodiment one of first and second electricallyconductive layers 22, 23 comprises a patterned composite layer having anon-uniform sheet resistance to the flow of electrons through the layerand the other has a uniform sheet resistance to the flow of electronsthrough the layer. By way of further example, in one embodiment one offirst and second electrically conductive layers 22, 23 has a gradedthickness or composition and a non-uniform sheet resistance to the flowof electrons through the layer and the other has a non-uniform sheetresistance to the flow of electrons through the layer with thenon-uniformity in the other sheet resulting from a graded thickness orgraded composition as described herein. Typically, first electricallyconductive layer 22 and second electrically conductive layer 23 eachhave a non-uniform sheet resistance to the flow of electrons through therespective layers. Without being bound by any particular theory, it ispresently believed that an effective variation in the sheet resistanceof electrically conductive layer 22, electrically conductive layer 23,or electrically conductive layer 22 and electrically conductive layer 23improves the switching performance of the device by controlling thevoltage drop in the conductive layer to provide uniform potential dropor a desired non-uniform potential drop across the device over an areaof the device at least 25% of the device area.

In general, electrical circuit modeling may be used to determine thesheet resistance distribution providing desired switching performance,taking into account the type of electrochromic device, the device shapeand dimensions, electrode characteristics, and the placement ofelectrical connections (e.g., bus bars) to the voltage source. The sheetresistance distribution, in turn, can be controlled, at least in part,by patterning a sublayer in the first and/or second electricallyconductive layer(s), and optionally grading the thickness of the firstand/or second electrically conductive layer(s), grading the compositionof the first and/or second electrically conductive layer(s), or somecombination of these.

In one exemplary embodiment, the electrochromic device is a rectangularelectrochromic window. Referring again to FIG. 1, in this embodimentfirst substrate 24 and second substrate 25 are rectangular panes ofglass or other transparent substrate and electrochromic device 1 has twobus bars 26, 27 located on opposite sides of first electrode layer 20and second electrode layer 21, respectively. When configured in thismanner, it is generally preferred that the resistance to the flow ofelectrons in first electrically conductive layer 22 generally increasewith increasing distance from bus bar 26 and that the resistance to theflow of electrons in second electrically conductive layer 23 generallyincrease with increasing distance from bus bar 27. This, in turn, can beeffected, for example, by patterning a sublayer in the firstelectrically conductive layer 22 to generally increase its sheetresistance as a function of increasing distance from bus bar 26 andpatterning a sublayer in the second electrically conductive layer 23 togenerally increase its sheet resistance as a function of increasingdistance from bus bar 27. Alternatively, this can be effected by gradingthe thickness or the composition of first electrically conductive layer22 to generally increase its sheet resistance as a function ofincreasing distance from bus bar 26 and grading the thickness or thecomposition in second electrically conductive layer 23 to generallyincrease its sheet resistance as a function of increasing distance frombus bar 27.

The multi-layer devices of the present invention may have a shape otherthan rectangular, may have more than two bus bars, and/or may not havethe bus bars on opposite sides of the device. For example, themulti-layer device may have a perimeter that is more generally aquadrilateral, or a shape with greater or fewer sides than four forexample, the multi-layer device may be triangular, pentagonal,hexagonal, etc., in shape. By way of further example, the multi-layerdevice may have a perimeter that is curved but lacks vertices, e.g.,circular, oval, etc. By way of further example, the multi-layer devicemay comprise three, four or more bus bars connecting the multi-layerdevice to a voltage source, or the bus bars, independent of number maybe located on non-opposing sides. In each of such instances, thepreferred resistance profile in the electrically conductive layer(s) mayvary from that which is described for the rectangular, two bus barconfiguration.

In general, however, and independent of whether the multi-layer devicehas a shape other than rectangular, there are more than two electricalconnections (e.g., bus bars), and/or the electrical connections (e.g.,bus bars) are on opposite sides of the device, the sheet resistance,R_(s), in the first electrically conductive layer 22, in the secondelectrically conductive layer 23, or in the first electricallyconductive layer 22 and the second electrically conductive layer 23 maybe plotted to join points of equal sheet resistance (i.e., isoresistancelines) as a function of (two-dimensional) position within the firstand/or second electrically conductive layer. Plots of this generalnature, sometimes referred to as contour maps, are routinely used incartography to join points of equal elevation. In the context of thepresent invention, a contour map of the sheet resistance, R_(s), in thefirst and/or second electrically conductive layer as a function of(two-dimensional) position within the first and/or second electricallyconductive layer preferably contains a series of isoresistance lines(also sometimes referred to as contour lines) and resistance gradientlines (lines perpendicular to the isoresistance lines). The sheetresistance along a gradient line in the first and/or second electricallyconductive layer(s) generally increase(s), generally decrease(s),generally increase(s) until it reaches a maximum and then generallydecrease(s), or generally decrease(s) until it reaches a minimum andthen generally increase(s).

FIGS. 2A-2E depict a contour map of the sheet resistance, R_(s), in anelectrically conductive layer (i.e., the first electrically conductivelayer, the second electrically conductive layer, or each of the firstand second electrically conductive layers) as a function of(two-dimensional) position within the electrically conductive layer forseveral exemplary embodiments of an electrochromic stack in accordancewith the present invention. In each of FIGS. 2A-2E, contour map 50depicts a set of sheet isoresistance curves 52 (i.e., curves along whichthe sheet resistance, R_(s), has a constant value) and a set ofresistance gradient curves 54 that are perpendicular to isoresistancecurves 52 resulting from an electrochromic stack having a perimeter thatis square (FIGS. 2A, 2B, and 2C) or circular (FIGS. 2D and 2E) andvarying numbers and locations of bus bars 26 and 27 in contact with thefirst and second electrically conductive layers (not labeled) of theelectrochromic stack. In FIG. 2A, the direction of the set of gradients54 indicates that the sheet resistance, R_(s), within the electricallyconductive layer progressively increases along the set of gradients 54and between west side 55 and east side 56 of the electrically conductivelayer in contact with bus bar 27. In FIG. 2B, the direction of gradient54A indicates that the sheet resistance, R_(s), within the electricallyconductive layer in contact with bus bar 27 progressively decreases fromsouthwest corner 57 to centroid 59 and then decreases from centroid 59to northeast corner 58. In FIG. 2C, the direction of the set ofgradients 54 indicate that the sheet resistance, R_(s), within theelectrically conductive layer in contact with bus bar 27 progressivelydecreases from the west side 60 and east side 61 to centroid 59 andprogressively increases from the top side 58 and bottom side 57 tocentroid 59; stated differently, sheet resistance, R_(s), forms a saddlelike form centered around centroid 59. In FIG. 2D, the direction ofgradients 54a and 54b indicates that the sheet resistance, R_(s), withinthe electrically conductive layer in contact with bus bar 27progressively decreases from each of positions 64 and 65 to centroid 59and progressively increases from each of positions 63 and 62 to centroid59; stated differently, sheet resistance, R_(s), forms a saddle likeform centered around centroid 59. In FIG. 2E, the direction of the setof gradients 54 indicates that the sheet resistance, R_(s), within theelectrically conductive layer in contact with bus bar 27 progressivelydecreases from the west side 55 to the east side 56. In one embodiment,for example, the gradient in sheet resistance is a constant. By way offurther example, in one embodiment, the gradient in sheet resistance isa constant and the substrate is rectangular in shape.

In one presently preferred embodiment, the ratio of the value of maximumsheet resistance, R_(max), to the value of minimum sheet resistance,R_(min), in the first electrically conductive layer is at least about1.25. In one exemplary embodiment, the ratio of the value of maximumsheet resistance, R_(max), to the value of minimum sheet resistance,R_(min), in the first electrically conductive layer is at least about1.5. In one exemplary embodiment, the ratio of the value of maximumsheet resistance, R_(max), to the value of minimum sheet resistance,R_(min), in the first electrically conductive layer is at least about 2.In one exemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 3. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 4. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 5. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 6. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 7. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 8. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 9. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 10.

In one embodiment, the non-uniformity in the sheet resistance of thefirst electrically conductive layer may be observed by comparing theratio of the average sheet resistance, R_(avg) in two different regionsof the first electrically conductive layer wherein the first and secondregions are each circumscribed by a convex polygon and each comprises atleast 25% of the surface area of the first electrically conductivelayer. For example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the first electrically conductivelayer , R¹ _(avg), to the average sheet resistance in a second region ofthe first electrically conductive layer, R² _(avg), is at least 1.25wherein each of the first and second regions is circumscribed by aconvex polygon, and each comprises at least 25% of the surface area ofthe first electrically conductive layer. This may be illustrated byreference to FIG. 3. First electrically conductive layer 22 comprisesconvex polygon A₁ and convex polygon B₁ and each circumscribes a regioncomprising at least 25% of the surface area of first electricallyconductive layer 22; in one embodiment, the ratio of the average sheetresistance, R¹ _(avg), in a first region of the first electricallyconductive layer bounded by convex polygon A₁ to the average sheetresistance, R² _(avg), in a second region of the first electricallyconductive layer bounded by convex polygon B₁ is at least 1.25. Asillustrated, convex polygon A₁ is a triangle and convex polygon B₁ is asquare merely for purposes of exemplification; in practice, the firstregion may be bounded by any convex polygon and the second region may bebounded by any convex polygon. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 1.5 wherein the first and second regionsare each circumscribed by a convex polygon and each comprises at least25% of the surface area of the first electrically conductive layer. Byway of further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the first electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe first electrically conductive layer, R² _(avg), is at least 2wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of the firstelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 3 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 25%of the surface area of the first electrically conductive layer. By wayof further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the first electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe first electrically conductive layer, R² _(avg), is at least 4wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of the firstelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 5 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 25%of the surface area of the first electrically conductive layer. By wayof further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the first electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe first electrically conductive layer, R² _(avg), is at least 6wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of the firstelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 7 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 25%of the surface area of the first electrically conductive layer. By wayof further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the first electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe first electrically conductive layer, R² _(avg), is at least 8wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of the firstelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 9 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 25%of the surface area of the first electrically conductive layer. By wayof further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the first electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe first electrically conductive layer, R² _(avg), is at least 10wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of the firstelectrically conductive layer. In one embodiment in each of theforegoing examples, the first and second regions are mutually exclusiveregions.

In one embodiment, the non-uniformity in the sheet resistance of thefirst electrically conductive layer may be observed by comparing theaverage sheet resistance, R_(avg) in four different regions of the firstelectrically conductive layer wherein the first region is contiguouswith the second region, the second region is contiguous with the thirdregion, the third region is contiguous with the fourth region, each ofthe regions is circumscribed by a convex polygon, and each comprises atleast 10% of the surface area of the first electrically conductivelayer. For example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the first electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe first electrically conductive layer, R² _(avg), is at least 1.25,the ratio of the average sheet resistance in the second region of thefirst electrically conductive layer, R² _(avg), to the average sheetresistance in a third region of the first electrically conductive layer,R³ _(avg), is at least 1.25, the ratio of the average sheet resistancein the third region of the first electrically conductive layer, R³_(avg), to the average sheet resistance in a fourth region of the firstelectrically conductive layer, R⁴ _(avg), is at least 1.25, wherein thefirst region is contiguous with the second region, the second region iscontiguous with the third region, the third region is contiguous withthe fourth region, each of the regions is circumscribed by a convexpolygon, and each comprises at least 10% of the surface area of thefirst electrically conductive layer. By way of further example, in onesuch embodiment, the ratio of the average sheet resistance in a firstregion of the first electrically conductive layer, R¹ _(avg), to theaverage sheet resistance in a second region of the first electricallyconductive layer, R² _(avg), is at least 1.5, the ratio of the averagesheet resistance in the second region of the first electricallyconductive layer, R² _(avg), to the average sheet resistance in a thirdregion of the first electrically conductive layer, R³ _(avg), is atleast 1.5, the ratio of the average sheet resistance in the third regionof the first electrically conductive layer, R³ _(avg), to the averagesheet resistance in a fourth region of the first electrically conductivelayer, R⁴ _(avg), is at least 1.5, wherein the first region iscontiguous with the second region, the second region is contiguous withthe third region, the third region is contiguous with the fourth region,each of the regions is circumscribed by a convex polygon, and eachcomprises at least 10% of the surface area of the first electricallyconductive layer. By way of further example, in one such embodiment, theratio of the average sheet resistance in a first region of the firstelectrically conductive layer, R¹ _(avg), to the average sheetresistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 2, the ratio of the average sheetresistance in the second region of the first electrically conductivelayer, R² _(avg), to the average sheet resistance in a third region ofthe first electrically conductive layer, R³ _(avg), is at least 2, theratio of the average sheet resistance in the third region of the firstelectrically conductive layer, R³ _(avg), to the average sheetresistance in a fourth region of the first electrically conductivelayer, R⁴ _(avg), is at least 2, wherein the first region is contiguouswith the second region, the second region is contiguous with the thirdregion, the third region is contiguous with the fourth region, each ofthe regions is circumscribed by a convex polygon, and each comprises atleast 10% of the surface area of the first electrically conductivelayer. In one embodiment in each of the foregoing examples, the first,second, third and fourth regions are mutually exclusive regions.

In one presently preferred embodiment, the second electricallyconductive layer has a sheet resistance, R_(s), to the flow ofelectrical current through the second electrically conductive layer thatvaries as a function of position in the second electrically conductivelayer. In one such embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 1.25. Inone exemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 1.5. Inone exemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 2. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 3. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 4. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 5. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 6. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 7. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 8. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 9. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 10.

In one embodiment, the non-uniformity in the sheet resistance of thesecond electrically conductive layer may be observed by comparing theratio of the average sheet resistance, R_(avg) in two different regionsof the second electrically conductive layer wherein the first and secondregions are each circumscribed by a convex polygon and each comprises atleast 25% of the surface area of the second electrically conductivelayer. For example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 1.25wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of thesecond electrically conductive layer. This may be illustrated byreference to FIGS. 3. Second electrically conductive layer 23 comprisesconvex polygon A and convex polygon B and each circumscribes a regioncomprising at least 25% of the surface area of second electricallyconductive layer 23; in one embodiment, the ratio of the average sheetresistance, R¹ _(avg), in a first region of the second electricallyconductive layer bounded by convex polygon A to the average sheetresistance, R² _(avg), in a second region of the second electricallyconductive layer bounded by convex polygon B is at least 1.25. Asillustrated, convex polygon A is a triangle and convex polygon B is asquare merely for purposes of exemplification; in practice, the firstregion may be bounded by any convex polygon and the second region may bebounded by any convex polygon. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the second electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the second electricallyconductive layer, R² _(avg), is at least 1.5 wherein the first andsecond regions are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the second electricallyconductive layer. By way of further example, in one such embodiment, theratio of the average sheet resistance in a first region of the secondelectrically conductive layer, R¹ _(avg), to the average sheetresistance in a second region of the second electrically conductivelayer, R² _(avg), is at least 2 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 25%of the surface area of the second electrically conductive layer. By wayof further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 3wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of thesecond electrically conductive layer. By way of further example, in onesuch embodiment, the ratio of the average sheet resistance in a firstregion of the second electrically conductive layer, R¹ _(avg), to theaverage sheet resistance in a second region of the second electricallyconductive layer, R² _(avg), is at least 4 wherein the first and secondregions are each circumscribed by a convex polygon and each comprises atleast 25% of the surface area of the second electrically conductivelayer. By way of further example, in one such embodiment, the ratio ofthe average sheet resistance in a first region of the secondelectrically conductive layer, R¹ _(avg), to the average sheetresistance in a second region of the second electrically conductivelayer, R² _(avg), is at least 5 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 25%of the surface area of the second electrically conductive layer. By wayof further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 6wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of thesecond electrically conductive layer. By way of further example, in onesuch embodiment, the ratio of the average sheet resistance in a firstregion of the second electrically conductive layer, R¹ _(avg), to theaverage sheet resistance in a second region of the second electricallyconductive layer, R² _(avg), is at least 7 wherein the first and secondregions are each circumscribed by a convex polygon and each comprises atleast 25% of the surface area of the second electrically conductivelayer. By way of further example, in one such embodiment, the ratio ofthe average sheet resistance in a first region of the secondelectrically conductive layer, R¹ _(avg), to the average sheetresistance in a second region of the second electrically conductivelayer, R² _(avg), is at least 8 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 25%of the surface area of the second electrically conductive layer. By wayof further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 9wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of thesecond electrically conductive layer. By way of further example, in onesuch embodiment, the ratio of the average sheet resistance in a firstregion of the second electrically conductive layer, R¹ _(avg), to theaverage sheet resistance in a second region of the second electricallyconductive layer, R² _(avg), is at least 10 wherein the first and secondregions are each circumscribed by a convex polygon and each comprises atleast 25% of the surface area of the second electrically conductivelayer. In one embodiment in each of the foregoing examples, the firstand second regions are mutually exclusive regions.

In one embodiment, the non-uniformity in the sheet resistance of thesecond electrically conductive layer may be observed by comparing theaverage sheet resistance, R_(avg) in four different regions of thesecond electrically conductive layer wherein the first region iscontiguous with the second region, the second region is contiguous withthe third region, the third region is contiguous with the fourth region,each of the regions is circumscribed by a convex polygon, and eachcomprises at least 10% of the surface area of the second electricallyconductive layer. For example, in one such embodiment, the ratio of theaverage sheet resistance in a first region of the second electricallyconductive layer, R¹ _(avg), to the average sheet resistance in a secondregion of the second electrically conductive layer, R² _(avg), is atleast 1.25, the ratio of the average sheet resistance in the secondregion of the second electrically conductive layer, R² _(avg), to theaverage sheet resistance in a third region of the second electricallyconductive layer, R³ _(avg), is at least 1.25, the ratio of the averagesheet resistance in the third region of the second electricallyconductive layer, R³ _(avg), to the average sheet resistance in a fourthregion of the second electrically conductive layer, R⁴ _(avg), is atleast 1.25, wherein the first region is contiguous with the secondregion, the second region is contiguous with the third region, the thirdregion is contiguous with the fourth region, each of the regions iscircumscribed by a convex polygon, and each comprises at least 10% ofthe surface area of the second electrically conductive layer. By way offurther example, in one such embodiment, the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 1.5,the ratio of the average sheet resistance in the second region of thesecond electrically conductive layer, R² _(avg), to the average sheetresistance in a third region of the second electrically conductivelayer, R³ _(avg), is at least 1.5, the ratio of the average sheetresistance in the third region of the second electrically conductivelayer, R³ _(avg), to the average sheet resistance in a fourth region ofthe second electrically conductive layer, R⁴ _(avg), is at least 1.5,wherein the first region is contiguous with the second region, thesecond region is contiguous with the third region, the third region iscontiguous with the fourth region, each of the regions is circumscribedby a convex polygon, and each comprises at least 10% of the surface areaof the second electrically conductive layer. By way of further example,in one such embodiment, the ratio of the average sheet resistance in afirst region of the second electrically conductive layer, R¹ _(avg), tothe average sheet resistance in a second region of the secondelectrically conductive layer, R² _(avg), is at least 2, the ratio ofthe average sheet resistance in the second region of the secondelectrically conductive layer, R² _(avg), to the average sheetresistance in a third region of the second electrically conductivelayer, R³ _(avg), is at least 2, the ratio of the average sheetresistance in the third region of the second electrically conductivelayer, R³ _(avg), to the average sheet resistance in a fourth region ofthe second electrically conductive layer, R⁴ _(avg), is at least 2,wherein the first region is contiguous with the second region, thesecond region is contiguous with the third region, the third region iscontiguous with the fourth region, each of the regions is circumscribedby a convex polygon, and each comprises at least 10% of the surface areaof the second electrically conductive layer. In one embodiment in eachof the foregoing examples, the first, second, third and fourth regionsare mutually exclusive regions.

In one presently preferred embodiment, first and second electricallyconductive layers 22, 23 have a sheet resistance, R_(s), to the flow ofelectrical current through the second electrically conductive layer thatvaries as a function of position in the first and second electricallyconductive layers. Although it is generally preferred in this embodimentthat the ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in the first and secondelectrically conductive layers be approximately the same, they may havedifferent values. For example, in one such embodiment, the ratio of thevalue of maximum sheet resistance, R_(max), to the value of minimumsheet resistance, R_(min), in the first electrically conductive layerhas a value that is at least twice as much as the ratio of the value ofmaximum sheet resistance, R_(max), to the value of minimum sheetresistance, R_(min), in the second electrically conductive layer. Moretypically, however, the ratio of the value of maximum sheet resistance,R_(max), to the value of minimum sheet resistance, R_(min), in the firstand second electrically conductive layers will be approximately the sameand each at least about 1.25. In one exemplary embodiment, the ratio ofthe value of maximum sheet resistance, R_(max), to the value of minimumsheet resistance, R_(min), the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first and second electrically conductive layers will beapproximately the same and each at least about 1.5. In one exemplaryembodiment, the ratio of the value of maximum sheet resistance, R_(max),to the value of minimum sheet resistance, R_(min), the ratio of thevalue of maximum sheet resistance, R_(max), to the value of minimumsheet resistance, R_(min), in each of the first and second electricallyconductive layers is at least about 2. In one exemplary embodiment, theratio of the value of maximum sheet resistance, R_(max), to the value ofminimum sheet resistance, R_(min), the ratio of the value of maximumsheet resistance, R_(max), to the value of minimum sheet resistance,R_(min), in each of the first and second electrically conductive layersis at least about 3. In one exemplary embodiment, the ratio of the valueof maximum sheet resistance, R_(max), to the value of minimum sheetresistance, R_(min), the ratio of the value of maximum sheet resistance,R_(max), to the value of minimum sheet resistance, R_(min), in each ofthe first and second electrically conductive layers is at least about 4.In one exemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),the ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in each of the first andsecond electrically conductive layers is at least about 5. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),the ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in each of the first andsecond electrically conductive layers is at least about 6. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),the ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in each of the first andsecond electrically conductive layers is at least about 7. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),the ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in each of the first andsecond electrically conductive layers is at least about 8. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),the ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in each of the first andsecond electrically conductive layers is at least about 9. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),the ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in each of the first andsecond electrically conductive layers is at least about 10.

In one embodiment, the non-uniformity in the sheet resistance of thefirst and second electrically conductive layers may be observed bycomparing the ratio of the average sheet resistance, R_(avg) in twodifferent regions of the first and second electrically conductivelayers, respectively, wherein the first and second regions of the firstelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the firstelectrically conductive layer and the first and second regions of thesecond electrically conductive layer are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of thesecond electrically conductive layer. For example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 1.25 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 1.25wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 1.5 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 1.5wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 2 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 2wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 3 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 3wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 4 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 4wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 5 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 5wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 6 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 6wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 7 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 7wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 8 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 8wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 9 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 9wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 10 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 10wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. In one embodiment in each of theforegoing examples, the first and second regions are mutually exclusiveregions.

Referring again to FIG. 3, the spatial non-uniformity of the sheetresistance of the first and second electrically conductive layer may becorrelated in accordance with one aspect of the present invention. Forexample, line segment X₁-Y₁ in first electrically conductive layer 22may be projected through second electrode layer 21, ion conductor layer10 and first electrode layer 20 and onto second electrically conductivelayer 23, with the projection defining line segment X-Y. In general, ifthe sheet resistance generally increases in first electricallyconductive layer 22 along line segment X₁-Y₁ (i.e., the sheet resistancegenerally increases moving along the sheet resistance gradient curve inthe direction from point X₁ to point Y₁), the sheet resistance generallydecreases in second electrically conductive layer 23 along segment X-Y(i.e., the sheet resistance generally decreases along sheet resistancegradient curve 54 and in the direction from point X to point Y). Aspreviously noted, line segments X-Y and X₁-Y₁ have a length of at least1 cm. For example, line segments X-Y and X₁-Y₁ may have a length of 2.5cm, 5 cm, 10 cm, or 25 cm. Additionally, line segments X-Y and X₁-Y₁ maybe straight or curved. In one embodiment, for example, the sheetresistance gradients in electrically conductive layers 22, 23 arenon-zero constants and are of opposite sign (e.g., the sheet resistancegenerally increases linearly in first electrically conductive layeralong in the direction from point X₁ to point Y₁ and generally decreaseslinearly along sheet resistance gradient curve 54 in the direction frompoint X to point Y). By way of further example, in one embodiment,substrates 24, 25 are rectangular and the sheet resistance gradients inelectrically conductive layers 22, 23 are non-zero constants and are ofopposite sign (e.g., the sheet resistance generally increases linearlyin second electrically conductive layer 23 along gradient 54 in thedirection from point X to point Y and generally decreases linearly infirst electrically conductive layer 22 along the line containing linesegment X₁-Y₁ in the direction from point X₁ to point Y₁).

In another embodiment, and still referring to FIG. 3, the spatialnon-uniformity of the sheet resistance of the first and secondelectrically conductive layers may be characterized by reference toseparate first and second regions in the first electrically conductivelayer and their projections onto the second electrically conductivelayer to define complementary first and second regions in the secondelectrically conductive layer wherein the first and second regions ofthe first electrically conductive layer are each bounded by a convexpolygon, each contain at least 25% of the surface area of the firstelectrically conductive layer, and are mutually exclusive regions. Ingeneral, the first electrically conductive layer has an average sheetresistance in the first and regions of the first electrically conductivelayer and the second electrically conductive layer has an average sheetresistance in the complementary first and second regions of the secondelectrically conductive layer wherein: (a) (i) a ratio of the averagesheet resistance of the first electrically conductive layer in the firstregion to the average sheet resistance of the first electricallyconductive layer in the second region is at least 1.5 or (ii) a ratio ofthe average sheet resistance of the second electrically conductive layerin the complementary first region to the average sheet resistance of thesecond electrically conductive layer in the complementary second regionis greater than 1.5 and (b) a ratio of the average sheet resistance ofthe first electrically conductive layer in the first region to theaverage sheet resistance of the second electrically layer in thecomplementary first region (i.e., the projection of the first region ofthe first electrically conductive layer onto the second electricallyconductive layer) is at least 150% of the ratio of the average sheetresistance of the first electrically conductive layer in the secondregion to the average sheet resistance of the second electrically layerin the complementary second region (i.e., the projection of the secondregion of the first electrically conductive layer onto the secondelectrically conductive layer).

Still referring to FIG. 3, first electrically conductive layer 22comprises a region A₁ and a region B₁ wherein region A₁ and region B₁each comprise at least 25% of the surface area of the first electricallyconductive layer, are each circumscribed by a convex polygon and aremutually exclusive regions. A projection of region A₁ onto secondelectrically conductive layer 23 defines a region A circumscribed by aconvex polygon in the second electrically conductive layer comprising atleast 25% of the surface area of the second electrically conductivelayer. A projection of region B₁ onto the second electrically conductivelayer defines a region B circumscribed by a convex polygon in the secondelectrically conductive layer comprising at least 25% of the surfacearea of the second electrically conductive layer. First electricallyconductive layer 22 has an average sheet resistance in region A₁corresponding to R^(A1) _(avg) and an average sheet resistance in regionB₁ corresponding to R^(B1) _(avg). Second electrically conductive layer23 has an average sheet resistance in region A corresponding to R^(A)_(avg) and an average sheet resistance in region B corresponding toR^(B) _(avg). In accordance with one embodiment, (i) the ratio of R^(A1)_(avg) to R^(B1) _(avg) or the ratio of R^(B) _(avg) to R^(A) _(avg) isat least 1.5 and (ii) the ratio of (R^(A1) _(avg)/R^(A) _(avg)) to(R^(B1) _(avg)/R^(B) _(avg)) is at least 1.5. For example, in oneembodiment, (i) the ratio of R^(A1) _(avg) to R^(B1) _(avg) or the ratioof R^(B) _(avg) to R^(A) _(avg) is at least 1.75 and (ii) the ratio of(R^(A1) _(avg)/R^(A) _(avg)) to (R^(B1) _(avg)/R^(B) _(avg)) is at least1.75. By way of further example, in one embodiment, (i) the ratio ofR^(A1) _(avg) to R^(B1) _(avg) or the ratio of R^(B) _(avg) to R^(A)_(avg) is at least 2 and (ii) the ratio of (R^(A1) _(avg)/R^(A) _(avg))to (R^(B1) _(avg)/R^(B) _(avg)) is at least 2. By way of furtherexample, in one embodiment, (i) the ratio of R^(A1) _(avg) to R^(B1)_(avg) or the ratio of R^(B) _(avg) to R^(A) _(avg) is at least 3 and(ii) the ratio of (R^(A1) _(avg)/R^(A) _(avg)) to (R^(B1) _(avg)/R^(B)_(avg)) is at least 3. By way of further example, in one embodiment, (i)the ratio of R^(A1) _(avg) to R^(B1) _(avg) or the ratio of R^(B) _(avg)to R^(A) _(avg) is at least 5 and (ii) the ratio of (R^(A1) _(avg)/R^(A)_(avg)) to (R^(B1) _(avg)/R^(B) _(avg)) is at least 5. By way of furtherexample, in one embodiment, (i) the ratio of R^(A1) _(avg) to R^(B1)_(avg) or the ratio of R^(B) _(avg) to R^(A) _(avg) is at least 10 and(ii) the ratio of (R^(A1) _(avg)/R^(A) _(avg)) to (R^(B1) _(avg)/R^(B)_(avg)) is at least 10.

Without wishing to be bound by any particular theory, and based uponcertain experimental evidence obtained to-date, in certain embodimentsthe electrode sheet resistance may be expressed as a function ofposition in a large area electrochromic device that provides a localvoltage drop across the electrochromic stack that is substantiallyconstant. For the simple geometry shown in FIG. 1, where the contact(bus bar 27) to the top electrode is made at x=0 and the contact (busbar 26) to the bottom electrode is made at x=xt, the relationship issimply that

R′(x)=R(x)*(xt/x−1);

where R(x) is the sheet resistance of the top electrode as a function ofposition and R′(x) is the sheet resistance of the bottom electrode as afunction of position. A simple mathematical example of this relationshipis that for a linear change in the sheet resistance of the topelectrode, R(x)=a*x, the sheet resistance of the bottom electrode mustbe R′(x)=a*(xt−x). Another simple example is that for R(x)=1/(xt−a*x)then R′(x)=1/(a*x). This relationship holds in a mathematical sense forany function R(x). This relationship can be generalized to any electrodesheet resistance distribution that smoothly varies and any contactconfiguration by the following relationship between the sheet resistancefrom one contact (z=0) to anther (z=L) along gradient curves that areperpendicular to iso-resistance lines R(z), and the correspondingopposing electrode sheet resistance distribution R′(z).

R′(z)=R(z)*(L/z−1);

As a practical matter, devices do not need to precisely adhere to thisrelationship to realize the benefits of this invention. For example, inthe case above where R′(x)=1/(a*x) , R′(0)=infinity. While one canpractically create resistances of very large magnitude, a film with aR′(x)=1/(a*x+b) where b is small relative to a can exhibit significantlyimproved switching uniformity over a device comprising electrodes ofuniform sheet resistance.

Electrically conductive layers having a non-uniform sheet resistance maybe prepared by a range of methods. In one embodiment, the non-uniformsheet resistance is the result of the patterning of two materials in theelectrically conductive layer(s). In another embodiment the non-uniformsheet resistance is the result of a composition variation; compositionvariations may be formed, for example, by sputter coating from twocylindrical targets of different materials while varying the power toeach target as a function of position relative to the substrate, byreactive sputter coating from a cylindrical target while varying the gaspartial pressure and/or composition as a function of position relativeto the substrate, by spray coating with a varying composition or processas a function of position relative to the substrate, or by introducing adopant variation to a uniform composition and thickness film by ionimplantation, diffusion, or reaction. In another embodiment, thenon-uniform sheet resistance is the result of a thickness variation inthe layer; thickness variations may be formed, for example, by sputtercoating from a cylindrical target while varying the power to the targetas a function of as a function of position relative to the substrate,sputter coating from a target at constant power and varying the velocityof substrate under the target as a function of as a function of positionrelative to the substrate, e.g., a deposited stack of uniform TCO filmson a substrate where each film has a limited spatial extent.Alternatively, a thickness gradient can be formed by starting with auniform thickness conductive layer and then etching the layer in a waythat is spatially non-uniform such as dip-etching or spraying withetchant at a non-uniform rate across the layer. In another embodiment,the non-uniform sheet resistance is the result of patterning; gradientsmay be introduced, for example, by laser patterning a series of scribesinto a constant thickness and constant resistivity film to create adesired spatially varying resistivity. In addition to laser patterning,mechanical scribing and lithographic patterning using photoresists (asknown in the art of semiconductor device manufacturing) can be used tocreate a desired spatially varying resistivity. In another embodiment,the non-uniform sheet resistance is the result of a defect variation; adefect variation may be introduced, for example, by introducingspatially varying defects via ion implantation, or creating a spatiallyvarying defect density via a spatially varying annealing process appliedto a layer with a previously uniform defect density.

To facilitate more rapid switching of electrochromic device 1 from astate of relatively greater transmittance to a state of relativelylesser transmittance, or vice versa, first current modulating structure30, second current modulating structure 31 or both first and secondcurrent modulating structures 30 and 31 comprise a resistive material(e.g., a material having a resistivity of at least about 10⁴Ω·cm) and atleast one of first and second current modulating structures 30, 31 has anon-uniform cross-layer resistance, R_(C), to the flow of electronsthrough the structure (i.e., in the case of first current modulatingstructures 30, the cross-layer resistance is measured in the directionfrom electrically conductive layer 22 to electrode layer 20 and in thecase of first current modulating structures 31, the cross-layerresistance is measured in the direction from electrically conductivelayer 23 to electrode layer 21; in each instance a direction that isnormal to the direction of the sheet resistance of electricallyconductive layers 23 and 23, respectively). In one such embodiment onlyone of first and second current modulating structures 30, 31 has anon-uniform cross-layer resistance, R_(C), to the flow of electronsthrough the layer. Alternatively, and more typically, first currentmodulating structure 30 and second current modulating structure 31 eachhave a non-uniform cross-layer resistance, R_(C), to the flow ofelectrons through the respective layers. Without being bound by anyparticular theory, it is presently believed that spatially varying thecross-layer resistance, R_(C), of first current modulating structure 30and second current modulating structure 31, spatially varying thecross-layer resistance, R_(C), of the first current modulating structure30, or spatially varying the cross-layer resistance, R_(C), of thesecond current modulating structure 31 improves the switchingperformance of the device by providing a more uniform potential drop ora desired non-uniform potential drop across the device, over the area ofthe device.

In one exemplary embodiment, current modulating structure 30 and/or 31is a composite comprising at least two materials possessing differentconductivities. For example, in one embodiment the first material is aresistive material having a resistivity in the range of about 10⁴Ω·cm to10¹⁰Ω·cm and the second material is an insulator. By way of furtherexample, in one embodiment the first material is a resistive materialhaving a resistivity of at least 10⁴Ω·cm and the second material has aresistivity that exceeds the resistivity of the first by a factor of atleast 10². By way of further example, in one embodiment the firstmaterial is a resistive material having a resistivity of at least10⁴Ω·cm and the second material has a resistivity that exceeds theresistivity of the first by a factor of at least 10³. By way of furtherexample, in one embodiment the first material is a resistive materialhaving a resistivity of at least 10⁴Ω·cm and the second material has aresistivity that exceeds the resistivity of the first by a factor of atleast 10⁴. By way of further example, in one embodiment the firstmaterial is a resistive material having a resistivity of at least10⁴Ω·cm and the second material has a resistivity that exceeds theresistivity of the first by a factor of at least 10⁵. By way of furtherexample, in one embodiment, at least one of current modulatingstructures 30, 31 comprises a first material having a resistivity in therange of 10⁴ to 10¹⁰Ω·cm and a second material that is an insulator orhas a resistivity in the range of 10¹⁰ to 10¹⁴Ω·cm. By way of furtherexample, in one embodiment, at least one of current modulatingstructures 30, 31 comprises a first material having a resistivity in therange of 10⁴ to 10¹⁰Ω·cm and a second material having a resistivity inthe range of 10¹⁰ to 10¹⁴Ω·cm wherein the resistivities of the first andsecond materials differ by a factor of at least 10³. By way of furtherexample, in one embodiment, at least one of current modulatingstructures 30, 31 comprises a first material having a resistivity in therange of 10⁴ to 10¹⁰Ω·cm and a second material having a resistivity inthe range of 10¹⁰ to 10¹⁴Ω·cm wherein the resistivities of the first andsecond materials differ by a factor of at least 10⁴. By way of furtherexample, in one embodiment, at least one of current modulatingstructures 30, 31 comprises a first material having a resistivity in therange of 10⁴ to 10¹⁰Ω·cm and a second material having a resistivity inthe range of 10¹⁰ to 10¹⁴Ω·cm wherein the resistivities of the first andsecond materials differ by a factor of at least 10⁵. In each of theforegoing exemplary embodiments, each of current modulating structures30, 31 may comprise a first material having a resistivity in the rangeof 10⁴ to 10¹⁰Ω·cm and a second material that is insulating.

Depending upon the application, the relative proportions of the firstand second materials in current modulating structure 30 and/or 31 mayvary substantially. In general, however, the second material (i.e., theinsulating material or material having a resistivity in the range of10¹⁰ to 10¹⁴Ω·cm) constitutes at least about 5 vol % of at least one ofcurrent modulating structures 30, 31. For example, in one embodiment thesecond material constitutes at least about 10 vol % of at least one ofcurrent modulating structures 30, 31. By way of further example, in oneembodiment the second material constitutes at least about 20 vol % of atleast one of current modulating structures 30, 31. By way of furtherexample, in one embodiment the second material constitutes at leastabout 30 vol % of at least one of current modulating structures 30, 31.By way of further example, in one embodiment the second materialconstitutes at least about 40 vol % of at least one of currentmodulating structures 30, 31. In general, however, the second materialwill typically not constitute more than about 70 vol % of either ofcurrent modulating structures 30, 31. In each of the foregoingembodiments and as previously discussed, the second material may have aresistivity in the range of 10¹⁰ to 10¹⁴Ω·cm and the resistivities ofthe first and second materials (in either or both of current modulatingstructures 30, 31) may differ by a factor of at least 10³.

In general, first and second current modulating structures 30, 31 maycomprise any material exhibiting sufficient resistivity, opticaltransparency, and chemical stability for the intended application. Forexample, in some embodiments, current modulating structures 30,31 maycomprise a resistive or insulating material with high chemicalstability. Exemplary insulator materials include alumina, silica, poroussilica, fluorine doped silica, carbon doped silica, silicon nitride,silicon oxynitride, hafnia, magnesium fluoride, magnesium oxide,poly(methyl methacrylate) (PMMA), polyimides, polymeric dielectrics suchas polytetrafluoroethylene (PTFE) and silicones. Exemplary resistivematerials include zinc oxide, zinc sulfide, titanium oxide, and gallium(III) oxide, yttrium oxide, zirconium oxide, aluminum oxide, indiumoxide, stannic oxide and germanium oxide. In one embodiment, one or bothof first and second current modulating structures 30, 31 comprise one ormore of such resistive materials. In another embodiment, one or both offirst and second current modulating structures 30, 31 comprise one ormore of such insulating materials. In another embodiment, one or both offirst and second current modulating structures 30, 31 comprise one ormore of such resistive materials and one or more of such insulatingmaterials.

The thickness of current modulating structures 30, 31 may be influencedby the composition of the material comprised by the structures and itsresistivity and transmissivity. In some embodiments, current modulatingstructures 30 and 31 are transparent and each have a thickness that isbetween about 50 nm and about 1 micrometer. In some embodiments, thethickness of current modulating structures 30 and 31 is between about100 nm and about 500 nm. In general, thicker or thinner layers may beemployed so long as they provide the necessary electrical properties(e.g., conductivity) and optical properties (e.g., transmittance). Forcertain applications it will generally be preferred that currentmodulating structures 30 and 31 be as thin as possible to increasetransparency and to reduce cost.

In general, electrical circuit modeling may be used to determine thecross-layer resistance distribution of the current modulating structuresto provide desired switching performance, taking into account the typeof electrochromic device, the device shape and dimensions, electrodecharacteristics, and the placement of electrical connections (e.g., busbars) to the voltage source. The cross-layer resistance distribution, inturn, can be controlled, at least in part, by patterning the firstand/or materials in the current modulating structure. In one embodiment,for example, the current modulating structure comprises a patternedlayer of an insulating material and a layer of a resistive material. Byway of further example, in one embodiment the current modulatingstructure is on the surface of an electrically conductive layer andcomprises a layer of a first material that is resistive and a patternedlayer of a second material that is insulating with the layer of theresistive first material being proximate the electrically conductivelayer and the patterned layer of the insulating material being distal tothe electrically conductive layer. By way of further example, in oneembodiment the current modulating structure is on the surface of anelectrically conductive layer and comprises a layer of a first materialthat is resistive and a patterned layer of a second material that isinsulating with the patterned layer of the insulating material beingproximate the electrically conductive layer and the layer of the firstresistive material being distal to the electrically conductive layer.

The cross-layer resistance of the current modulating structure may bevaried as a function of position by a range of techniques. FIGS. 4-9illustrate various embodiments in which the cross-layer resistance of acurrent modulating structure may be varied as a function of position bypatterning a layer of a resistive material with a layer of insulatingmaterial.

FIG. 4 illustrates two exemplary patterns (right column) that may beachieved by patterning a layer of a first material 71 and a secondmaterial 70 having a resistivity at least two orders of magnitudegreater than the first material on a transparent conductive oxide (TCO)layer 73 supported by a substrate. In each of these embodiments, thesecond material 70 is deposited on the TCO layer 73 or the firstmaterial 71 in a predetermined pattern and the first material (i)overcoats the TCO but not the second material or (ii) overcoats thesecond material and fills the gaps between regions of the secondmaterial deposited on the TCO. In the top right panel of FIG. 4,circular regions of resistive but not insulating material and in thebottom right panel of FIG. 4 rectangular regions containing resistivebut not insulating material increase in size relative to a background ofinsulating material as a function of distance from two opposing edgesand reach a maximum size at the midline (or midpoint) between the busbars of a multi-layer device (not shown) comprising the currentmodulating structure.

FIG. 5 illustrates two exemplary patterns (right column) that may beachieved by patterning a layer of a first material 71 and a secondmaterial 70 having a resistivity at least two orders of magnitudegreater than the first material on a transparent conductive oxide (TCO)layer 73 supported by a substrate. In each of these embodiments, thesecond material 70 is deposited on the TCO layer 73 or the firstmaterial 71 in a predetermined pattern and the first material (i)overcoats the TCO but not the second material or (ii) overcoats thesecond material and fills the gaps between regions of the secondmaterial deposited on the TCO. In the top right panel of FIG. 5,“diamond-shaped” regions (top right panel) containing resistive but notinsulating material and “stair-stepped” regions of resistive material(bottom right panel) containing resistive but not insulating materialincrease in size relative to a background of insulating material as afunction of distance from two opposing edges and reach a maximum size atthe midline (or midpoint) between the bus bars of a multi-layer device(not shown) comprising the current modulating structure.

FIG. 6 illustrates an exemplary pattern that may be achieved bypatterning a layer of a first material 71 and a second material 70having a resistivity at least two orders of magnitude greater than thefirst material on a transparent conductive oxide (TCO) layer 73supported by a substrate 72. In this embodiment, the second material 70is deposited on the TCO layer 73 or the first material 71 in apredetermined pattern and the first material (i) overcoats the TCO butnot the second material or (ii) overcoats the second material and fillsthe gaps between regions of the second material deposited on the TCO. Inthe right hand panel of FIG. 6, populations of circles of resistivematerial increase in number density (but not necessarily size) relativeto a background of insulating material as a function of distance fromtwo opposing edges and reach a maximum population density at the midline(or midpoint) between the bus bars of a multi-layer device (not shown)comprising the current modulating structure.

FIG. 7 illustrates an exemplary pattern that may be achieved bypatterning a layer of a first material 71 and a second material 70having a resistivity at least two orders of magnitude greater than thefirst material on a transparent conductive oxide (TCO) layer 73supported by a substrate 72. In this embodiment, the second material 70is deposited on the TCO layer 73 or the first material 71 in apredetermined pattern and the first material (i) overcoats the TCO butnot the second material or (ii) overcoats the second material and fillsthe gaps between regions of the second material deposited on the TCO. Inthe right hand panel of FIG. 7 a series of lines of resistive materialincrease in width relative to a background of insulating material as afunction of distance from two opposing edges and reach a maximum widthat the midline (or midpoint) between the bus bars of a multi-layerdevice (not shown) comprising the current modulating structure.

FIG. 8 illustrates an exemplary pattern that may be achieved bypatterning a layer of a first material 71 and a second material 70having a resistivity at least two orders of magnitude greater than thefirst material on a transparent conductive oxide (TCO) layer 73supported by a substrate 72. In this embodiment, the second material 70is deposited on the TCO layer 73 or the first material 71 in apredetermined pattern and the first material (i) overcoats the TCO butnot the second material or (ii) overcoats the second material and fillsthe gaps between regions of the second material deposited on the TCO. Inthe right hand panel of FIG. 8, populations of lines of resistivematerial increase in number density (but not necessarily size) relativeto a background of insulating material as a function of distance fromtwo opposing edges and reach a maximum population density at the midline(or midpoint) between the bus bars of a multi-layer device (not shown)comprising the current modulating structure.

FIG. 9 illustrates an exemplary pattern that may be achieved bypatterning a layer of a first material 71 and a second material 70having a resistivity at least two orders of magnitude greater than thefirst material on a Transparent conductive oxide (TCO) layer 73supported by a substrate 72. In this embodiment, the second material 70is deposited on the TCO layer 73 or the first material 71 in apredetermined pattern and the first material (i) overcoats the TCO butnot the second material or (ii) overcoats the second material and fillsthe gaps between regions of the second material deposited on the TCO. Inthe right hand panel of FIG. 9 hexagon-shaped deposits of resistivematerial decrease in size relative to a background of insulatingmaterial as a function of distance from two opposing edges and reach aminimum size at the midline (or midpoint) between the bus bars of amulti-layer device (not shown) comprising the current modulatingstructure.

In each of the embodiments illustrated in FIGS. 4-9, the fraction ofinsulating material per unit area decreases as a function of distancefrom the opposing top and bottom edges and reaches a minimum at themidline (or midpoint) between the bus bars of a multi-layer device (notshown) comprising the current modulating structure where the fraction ofinsulating material in an area is at a minimum.

In general, the cross-layer resistance R_(C), in the first currentmodulating structure 30, in the second current modulating structure 31,or in the first current modulating structure 30 and the second currentmodulating structure 31 may be plotted to join points of equalcross-layer resistance R_(C), (i.e., isoresistance lines) as a functionof (two-dimensional) position within the first and/or second currentmodulating structure. Plots of this general nature, sometimes referredto as contour maps, are routinely used in cartography to join points ofequal elevation. In the context of the present invention, a contour mapof the cross-layer resistance R_(C), in the first and/or second currentmodulating structure as a function of (two-dimensional) position withinthe first and/or second current modulating structure preferably containsa series of isoresistance lines (also sometimes referred to as contourlines) and resistance gradient lines (lines perpendicular to theisoresistance lines). The cross-layer resistance R_(C), along a gradientline in the first and/or second electrically conductive layer(s)generally increase(s), generally decrease(s), generally increase(s)until it reaches a maximum and then generally decrease(s), or generallydecrease(s) until it reaches a minimum and then generally increase(s).In one such embodiment, the cross-layer resistance R_(C), along agradient line in the first and/or second electrically conductivelayer(s) generally increase(s) parabolically, generally decrease(s)parabolically, generally increase(s) parabolically until it reaches amaximum and then generally decrease(s) parabolically, or generallydecrease(s) parabolically until it reaches a minimum and then generallyincrease(s) parabolically.

FIGS. 10A-E depict a contour map of the cross-layer resistance, R_(C),in a current modulating structure (i.e., the first current modulatingstructure, the second current modulating structure, or each of the firstand second current modulating structures as a function of(two-dimensional) position within the current modulating structure forseveral exemplary embodiments of an electrochromic stack in accordancewith the present invention. In each of FIGS. 10A-E, contour map 50depicts a set of cross-layer resistance, R_(C), curves 52 (i.e., curvesalong which the cross-layer resistance, R_(C), has a constant value) anda set of resistance gradient curves 54 that are perpendicular toisoresistance curves 52 resulting from an electrochromic stack having aperimeter that is square (FIGS. 10A, 10B and 10C) or circular (FIGS. 10Dand 10E) and varying numbers and locations of bus bars 26 and 27 incontact with the first and second electrically conductive layers (notlabeled) of the electrochromic stack. In FIG. 10A, the direction of theset of gradients 54 indicates that the cross-layer resistance, R_(C),through the current modulating structure progressively increases alongthe set of gradients 54 and between west side 55 and east side 56 of thethe current modulating structure in contact with bus bar 27. In FIG. 10Bthe direction of gradient 54A indicates that the cross-layer resistance,R_(C), through the current modulating structure in contact with bus bar27 progressively decreases from southwest corner 57 to centroid 59 andthen decreases from centroid 59 to northeast corner 58. In FIG. 10C, thedirection of the set of gradients 54 indicate that the cross-layerresistance, R_(C), through the current modulating structure in contactwith bus bar 27 progressively decreases from the west side 60 and eastside 61 to centroid 59 and progressively increases from the top side 58and bottom side 57 to centroid 59; stated differently, the cross-layerresistance, R_(C), through the current modulating structure forms asaddle like form centered around centroid 59. In FIG. 10D, the directionof gradients 54a and 54b indicates that the cross-layer resistance,R_(C), through the current modulating structure in contact with bus bar27 progressively decreases from each of positions 64 and 65 to centroid59 and progressively increases from each of positions 63 and 62 tocentroid 59; stated differently, the cross-layer resistance, R_(C),through the current modulating structure forms a saddle like formcentered around centroid 59. In FIG. 10E, the direction of the set ofgradients 54 indicates that the cross-layer resistance, R_(C), throughthe current modulating structure in contact with bus bar 27progressively decreases from the west side 55 to the east side 56. Inone embodiment, for example, the cross-layer resistance, R_(C), throughthe voltage modulating is a constant. By way of further example, in oneembodiment, the gradient in the cross-layer resistance, R_(C), throughthe current modulating structure is a constant and the substrate isrectangular in shape.

In one embodiment, the non-uniformity in the cross-layer resistanceR_(C) of the first current modulating structure may be observed bycomparing the ratio of the average cross-layer resistance, R_(C-avg)through two different regions of the first current modulating structurewherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 10% of the surface area of the firstcurrent modulating structure. For example, in one such embodiment, theratio of the average cross-layer resistance through a first region ofthe first current modulating structure, R¹ _(C-avg), to the averagecross-layer resistance through a second region of the first currentmodulating structure, R² _(C-avgavg), is at least 1.25 wherein each ofthe first and second regions is circumscribed by a convex polygon, andeach comprises at least 10% of the surface area of the first currentmodulating structure. This may be illustrated by reference to FIG. 11.First current modulating structure 30 comprises convex polygon A₁ andconvex polygon B₁ and each circumscribes a region comprising at least10% of the surface area of first current modulating structure 30; in oneembodiment, the ratio of the average cross-layer resistance, R¹_(C-avg), through a first region of the first current modulatingstructure bounded by convex polygon A₁ to the average cross-layerresistance, R² _(C-avg), through a second region of the first currentmodulating structure bounded by convex polygon B₁ is at least 1.25. Asillustrated, convex polygon A₁ is a triangle and convex polygon B₁ is asquare merely for purposes of exemplification; in practice, the firstregion may be bounded by any convex polygon and the second region may bebounded by any convex polygon. By way of further example, in one suchembodiment, the ratio of the average cross-layer resistance through afirst region of the first current modulating structure, R¹ _(C-avg), tothe average cross-layer resistance through a second region of the firstcurrent modulating structure, R² _(C-avg), is at least 1.5 wherein thefirst and second regions are each circumscribed by a convex polygon andeach comprises at least 10% of the surface area of the first currentmodulating structure. By way of further example, in one such embodiment,the ratio of the average cross-layer resistance through a first regionof the first current modulating structure, R¹ _(C-avg), to the averagecross-layer resistance through a second region of the first currentmodulating structure, R² _(C-avg), is at least 2 wherein the first andsecond regions are each circumscribed by a convex polygon and eachcomprises at least 10% of the surface area of the first currentmodulating structure. By way of further example, in one such embodiment,the ratio of the average cross-layer resistance through a first regionof the first current modulating structure, R¹ _(C-avg), to the averagecross-layer resistance through a second region of the first currentmodulating structure, R² _(C-avg), is at least 3 wherein the first andsecond regions are each circumscribed by a convex polygon and eachcomprises at least 10% of the surface area of the first currentmodulating structure. In one embodiment in each of the foregoingexamples, the first and second regions are mutually exclusive regions.

In one embodiment, the non-uniformity in the cross-layer resistanceR_(C) of the second current modulating structure may be observed bycomparing the ratio of the average cross-layer resistance, R_(C-avg)through two different regions of the second current modulating structure31 wherein the first and second regions are each circumscribed by aconvex polygon and each comprises at least 10% of the surface area ofthe first current modulating structure. For example, in one suchembodiment, the ratio of the average cross-layer resistance through afirst region of the second current modulating structure 31, R¹ _(C-avg),to the average cross-layer resistance through a second region of thesecond current modulating structure, R² _(C-avg), is at least 1.25wherein each of the first and second regions is circumscribed by aconvex polygon, and each comprises at least 10% of the surface area ofthe first current modulating structure. This may be illustrated byreference to FIG. 11. Second current modulating structure 31 comprisesconvex polygon A and convex polygon B and each circumscribes a regioncomprising at least 10% of the surface area of second current modulatingstructure 31; in one embodiment, the ratio of the average cross-layerresistance, R¹ _(C-avg), through a first region of the second currentmodulating structure bounded by convex polygon A to the averagecross-layer resistance, R² _(C-avg), through a second region of thesecond current modulating structure bounded by convex polygon B is atleast 1.25. As illustrated, convex polygon A is a triangle and convexpolygon B is a square merely for purposes of exemplification; inpractice, the first region may be bounded by any convex polygon and thesecond region may be bounded by any convex polygon. By way of furtherexample, in one such embodiment, the ratio of the average cross-layerresistance through a first region of the second current modulatingstructure, R¹ _(C-avg), to the average cross-layer resistance through asecond region of the second current modulating structure, R²_(C-avgavg), is at least 1.5 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 10%of the surface area of the first current modulating structure. By way offurther example, in one such embodiment, the ratio of the averagecross-layer resistance through a first region of the second currentmodulating structure, R¹ _(C-avg), to the average cross-layer resistancethrough a second region of the second current modulating structure, R²_(C-avg), is at least 2 wherein the first and second regions are eachcircumscribed by a convex polygon and each comprises at least 10% of thesurface area of the second current modulating structure. By way offurther example, in one such embodiment, the ratio of the averagecross-layer resistance through a first region of the second currentmodulating structure, R¹ _(C-avg), to the average cross-layer resistancethrough a second region of the second current modulating structure, R²_(C-avg), is at least 3 wherein the first and second regions are eachcircumscribed by a convex polygon and each comprises at least 10% of thesurface area of the first current modulating structure. In oneembodiment in each of the foregoing examples, the first and secondregions are mutually exclusive regions.

In one presently preferred embodiment, the ratio of the value of maximumcross-layer resistance, R_(C-max), to the value of minimum cross-layerresistance, R_(C-min), in the first current modulating structure 30, thesecond current modulating structure 31, or both the first currentmodulating structure 30 and the second current modulating structure 31is at least about 1.25. In one exemplary embodiment, the ratio of thevalue of maximum cross-layer resistance, R_(C-max), to the value ofminimum cross-layer resistance, R_(C-min), in the first currentmodulating structure 30, the second current modulating structure 31, orboth the first current modulating structure 30 and the second currentmodulating structure 31 is at least about 2. In one exemplaryembodiment, the ratio of the value of maximum cross-layer resistance,R_(C-max), to the value of minimum cross-layer resistance, R_(C-min), inthe first current modulating structure 30, the second current modulatingstructure 31, or both the first current modulating structure 30 and thesecond current modulating structure 31 is at least about 3.

FIG. 12 illustrates one alternative embodiment of the present invention.Moving outward from the center, electrochromic device 1 comprises an ionconductor layer 10. First electrode layer 20 is on one side of and incontact with a first surface of ion conductor layer 10, and secondelectrode layer 21 is on the other side of and in contact with a secondsurface of ion conductor layer 10. The central structure, that is,layers 20, 10, 21, is positioned between first and second electricallyconductive layers 22 and 23 which, in turn, are arranged against outersubstrates 24, 25. Each of first and second electrically conductivelayers 22 and 23 are patterned layers comprising first material 34(e.g., a transparent conductive oxide) and second material 35 having aresistivity at least two orders of magnitude greater than the firstmaterial. Each of first and second electrically conductive layers 22 and23, in turn, are arranged against outer substrates 24, 25. In addition,electrochromic device 1 comprises current modulating structure 30between first electrically conductive layer 22 and first electrode 20.Current modulating structure 30 contains a resistive material and isgraded in thickness, with the thickness generally decreasingparabolically as a function of increasing thickness from bus bars 26, 27and reaching a minimum thickness at the midpoint (or midline) betweenbus bars 26, 27. Ion conductor layer 10 and, to a lesser extent, firstelectrode layer 20, compensate for the curvature of first currentmodulating structure 30 resulting from the thickness variation.

FIG. 13 illustrates one alternative embodiment of the present invention.Moving outward from the center, electrochromic device 1 comprises an ionconductor layer 10. First electrode layer 20 is on one side of and incontact with a first surface of ion conductor layer 10, and secondelectrode layer 21 is on the other side of and in contact with a secondsurface of ion conductor layer 10. The central structure, that is,layers 20, 10, 21, is positioned between first and second electricallyconductive layers 22 and 23 which, in turn, are arranged against outersubstrates 24, 25. Each of first and second electrically conductivelayers 22 and 23 are patterned layers comprising first material 34(e.g., a transparent conductive oxide) and second material 35 having aresistivity at least two orders of magnitude greater than the firstmaterial. Each of first and second electrically conductive layers 22 and23, in turn, are arranged against outer substrates 24, 25. In addition,electrochromic device 1 comprises current modulating structure 30between first electrically conductive layer 22 and first electrode 20.Current modulating structure 30 comprises first material 32 (e.g., aresistive material) and second material 33 having a resistivity at leasttwo orders of magnitude greater than the first material. In one furtherembodiment, electrochromic device 1 may additionally contain a secondcurrent modulating structure 31 (not shown) between second electrodelayer 21 and second electrically conductive layer 23; in one suchembodiment, the second current modulating structure may have a uniformor non-uniform cross-layer resistance as a function of position and, ifnon-uniform, the second current modulating structure may optionallycontained a patterned sublayer comparable to first current modulatingstructure 30.

Referring now to FIG. 14, in a further alternative embodiment, firstmaterial 32 (of electrochromic device 1 illustrated in FIG. 13) issubdivided into a multi-layer composite comprising sublayers a, b, c, d,and e in order to minimize conductive defects that may shunt layer 22 tolayer 20, and to improve the ohmic contact between first material 32 andfirst electrode layer 20, and between first material 32 and firstelectrically conductive layer 22. Layers a and e function as conductionband coupling layers that improve the ohmic contact between electricallyconductive layer 22 and layer d, and between layer b and electricalpotential smoothing layer 74, respectively. Layer c is a defectmitigation layer, separating layers b and d, each of which comprises aresistive material (as previously described in connection with firstmaterial 32). For example, in one embodiment layer c may be an ALD(atomic layer deposition) film of Al₂O₃ HfO₂, HfSiO, La₂O₃, SiO₂, STO,Ta₂O₅, TiO₂, ZnO or similar insulating or resistive materials. Layers aand e may be a metal, an oxide or a nitride material that has aconduction band energy which is between the conduction band energy offirst electrically conductive layer 22 and layer d, and betweenelectrical potential smoothing layer 74 and layer b, respectively, suchas an oxide or nitride with a conduction band energy between 3.5 and 5eV, such as SnO₂, ZnO, TiO₂, ZrO₂.

In certain embodiments, the patterning of the first and second materialsin current modulating structure 30 and/or 31 may cause a significantlocal variation in the electrical potential at the surface(s) thereof.Still referring to FIG. 14, this local variation in electrical potentialmay be reduced, for example, by incorporating an electrical potentialsmoothing layer 74 between first electrode layer 20 and currentmodulating structure 30. Electrical potential smoothing layer 74 maycomprise a thin layer of ITO, AZO, IZO or other transparent conductivematerial. Preferably, the thickness and conductivity of the electricalpotential smoothing layer 74 does not significantly affect the overallcross-layer resistance. For example, in one embodiment the smoothinglayer is a 10 nm thick sputtered film of ITO.

For exemplification purposes, FIG. 15 graphically correlates fillfactors required to achieve uniform switching for a range of resistormaterial resistivities (10⁵, 10⁷, and 10⁹Ωcm) and two different currentmodulating structure (composite layer) thicknesses as a function ofposition in a device having a surface area of 1 m². In this context, a“fill factor” is defined as the local fraction of the area thatcomprises insulating material. For example, a fill factor of one (1)indicates that there are no holes in the insulator material, a fillfactor of 0.5 correlates to a layer that is half-insulator and half-resistor, and a layer with a fill factor of zero (0) has only resistivematerial with no insulator material present locally in the layer.

For exemplification purposes, FIG. 16 graphically correlates theresistor layer thickness required in a current modulating structure tocompensate two different electrically conductive (e.g., TCO) layershaving a non-uniform sheet resistance where the electrically conductivelayer (TCO layer) has a functional form of sheet resistance as ax+b,where x is the location in the film on a substrate of size L. Theshallower curve corresponds to the case where a*L is much larger than band the steeper curve corresponds to the case where a*L is not muchlarger than b.

Referring again to FIG. 1, at least one of first and second electrodelayers 20 and 21 is electrochromic, one of the first and secondelectrode layers is the counter electrode for the other, and first andsecond electrode layers 20 and 21 are inorganic and/or solid.Non-exclusive examples of electrochromic electrode layers 20 and 21 arecathodically coloring thin films of oxides based on tungsten,molybdenum, niobium, titanium, lead and/or bismuth, or anodicallycoloring thin films of oxides, hydroxides and/or oxy-hydrides based onnickel, iridium, iron, chromium, cobalt and/or rhodium.

In one embodiment, first electrode layer 20 contains any one or more ofa number of different electrochromic materials, including metal oxides.Such metal oxides include tungsten oxide (WO₃), molybdenum oxide (MoO₃),niobium oxide (Nb₂O₅), titanium oxide (TiO₂), copper oxide (CuO),iridium oxide (Ir₂O₃), chromium oxide (Cr₂O₃), manganese oxide (Mn₂O₃),vanadium oxide (V₂O₃), nickel oxide (Ni₂O₃), cobalt oxide (Co₂O₃) andthe like. In some embodiments, the metal oxide is doped with one or moredopants such as lithium, sodium, potassium, molybdenum, vanadium,titanium, and/or other suitable metals or compounds containing metals.Mixed oxides (e.g., W—Mo oxide, W—V oxide) are also used in certainembodiments.

In some embodiments, tungsten oxide or doped tungsten oxide is used forfirst electrode layer 20. In one embodiment, first electrode layer 20 iselectrochromic and is made substantially of WO_(x), where “x” refers toan atomic ratio of oxygen to tungsten in the electrochromic layer, and xis between about 2.7 and 3.5. It has been suggested that onlysub-stoichiometric tungsten oxide exhibits electrochromism; i.e.,stoichiometric tungsten oxide, WO₃, does not exhibit electrochromism. Ina more specific embodiment, WO_(x), where x is less than 3.0 and atleast about 2.7 is used for first electrode layer 20. In anotherembodiment, first electrode layer 20 is WO_(x), where x is between about2.7 and about 2.9. Techniques such as Rutherford BackscatteringSpectroscopy (RBS) can identify the total number of oxygen atoms whichinclude those bonded to tungsten and those not bonded to tungsten. Insome instances, tungsten oxide layers where x is 3 or greater exhibitelectrochromism, presumably due to unbound excess oxygen along withsub-stoichiometric tungsten oxide. In another embodiment, the tungstenoxide layer has stoichiometric or greater oxygen, where x is 3.0 toabout 3.5.

In certain embodiments, the electrochromic mixed metal oxide iscrystalline, nanocrystalline, or amorphous. In some embodiments, thetungsten oxide is substantially nanocrystalline, with grain sizes, onaverage, from about 5 nm to 50 nm (or from about 5 nm to 20 nm), ascharacterized by transmission electron microscopy (TEM). The tungstenoxide morphology may also be characterized as nanocrystalline usingx-ray diffraction (XRD); XRD. For example, nanocrystallineelectrochromic tungsten oxide may be characterized by the following XRDfeatures: a crystal size of about 10 to 100 nm (e.g., about 55 nm.Further, nanocrystalline tungsten oxide may exhibit limited long rangeorder, e.g., on the order of several (about 5 to 20) tungsten oxide unitcells.

The thickness of the first electrode layer 20 depends on theelectrochromic material selected for the electrochromic layer. In someembodiments, first electrode layer 20 is about 50 nm to 2,000 nm, orabout 100 nm to 700 nm. In some embodiments, the first electrode layer20 is about 250 nm to about 500 nm.

Second electrode layer 21 serves as the counter electrode to firstelectrode layer 20 and, like first electrode layer 20, second electrodelayer 21 may comprise electrochromic materials as well asnon-electrochromic materials. Non-exclusive examples of second electrodelayer 21 are cathodically coloring electrochromic thin films of oxidesbased on tungsten, molybdenum, niobium, titanium, lead and/or bismuth,anodically coloring electrochromic thin films of oxides, hydroxidesand/or oxy-hydrides based on nickel, iridium, iron, chromium, cobaltand/or rhodium, or non-electrochromic thin films, e.g., of oxides basedon vanadium and/or cerium as well as activated carbon. Also combinationsof such materials can be used as second electrode layer 21.

In some embodiments, second electrode layer 21 may comprise one or moreof a number of different materials that are capable of serving asreservoirs of ions when the electrochromic device is in the bleachedstate. During an electrochromic transition initiated by, e.g.,application of an appropriate electric potential, the counter electrodelayer transfers some or all of the ions it holds to the electrochromicfirst electrode layer 20, changing the electrochromic first electrodelayer 20 to the colored state.

In some embodiments, suitable materials for a counter electrodecomplementary to WO₃ include nickel oxide (NiO), nickel tungsten oxide(NiWO), nickel vanadium oxide, nickel chromium oxide, nickel aluminumoxide, nickel manganese oxide, nickel magnesium oxide, chromium oxide(Cr₂O₃), manganese oxide (MnO₂), and Prussian blue. Optically passivecounter electrodes comprise cerium titanium oxide (CeO₂—TiO₂), ceriumzirconium oxide (CeO₂—ZrO₂), nickel oxide (NiO), nickel-tungsten oxide(NiWO), vanadium oxide (V₂O₅), and mixtures of oxides (e.g., a mixtureof Ni₂O₃ and WO₃). Doped formulations of these oxides may also be used,with dopants including, e.g., tantalum and tungsten. Because firstelectrode layer 20 contains the ions used to produce the electrochromicphenomenon in the electrochromic material when the electrochromicmaterial is in the bleached state, the counter electrode preferably hashigh transmittance and a neutral color when it holds significantquantities of these ions.

In some embodiments, nickel-tungsten oxide (NiWO) is used in the counterelectrode layer. In certain embodiments, the amount of nickel present inthe nickel—tungsten oxide can be up to about 90% by weight of thenickel-tungsten oxide. In a specific embodiment, the mass ratio ofnickel to tungsten in the nickel-tungsten oxide is between about 4:6 and6:4 (e.g., about 1:1). In one embodiment, the NiWO is between about 15%(atomic) Ni and about 60% Ni; between about 10% W and about 40% W; andbetween about 30% O and about 75% O). In another embodiment, the NiWO isbetween about 30% (atomic) Ni and about 45% Ni; between about 10% W andabout 25% W; and between about 35% O and about 50% O. In one embodiment,the NiWO is about 42% (atomic) Ni, about 14% W, and about 44% O.

In some embodiments, the thickness of second electrode layer 21 is about50 nm about 650 nm. In some embodiments, the thickness of secondelectrode layer 21 is about 100 nm to about 400 nm, preferably in therange of about 200 nm to 300 nm.

Ion conducting layer 10 serves as a medium through which ions aretransported (in the manner of an electrolyte) when the electrochromicdevice transforms between the bleached state and the colored state. Ionconductor layer 10 comprises an ion conductor material. It may betransparent or non-transparent, colored or non-colored, depending on theapplication. Preferably, ion conducting layer 10 is highly conductive tothe relevant ions for the first and second electrode layers 20 and 21.Depending on the choice of materials, such ions include lithium ions(Li⁺) and hydrogen ions (H⁺) (i.e., protons). Other ions may also beemployed in certain embodiments. These include deuterium ions (D⁺),sodium ions (Na⁺), potassium ions (K⁺), calcium ions (Ca⁺⁺), barium ions(Ba⁺⁺), strontium ions (Sr⁺⁺), and magnesium ions (Mg⁺⁺). Preferably,ion conducting layer 10 also has sufficiently low electron conductivitythat negligible electron transfer takes place during normal operation.In various embodiments, the ion conductor material has an ionicconductivity of between about 10⁻⁵ S/cm and 10⁻³ S/cm .

Some non-exclusive examples of electrolyte types are: solid polymerelectrolytes (SPE), such as poly(ethylene oxide) with a dissolvedlithium salt; gel polymer electrolytes (GPE), such as mixtures ofpoly(methyl methacrylate) and propylene carbonate with a lithium salt;composite gel polymer electrolytes (CGPE) that are similar to GPE's butwith an addition of a second polymer such a poly(ethylene oxide), andliquid electrolytes (LE) such as a solvent mixture of ethylenecarbonate/diethyl carbonate with a lithium salt; and compositeorganic-inorganic electrolytes (CE), comprising an LE with an additionof titania, silica or other oxides. Some non-exclusive examples oflithium salts used are LiTFSI (lithium bis(trifluoromethane)sulfonimide), LiBF₄ (lithium tetrafluoroborate), LiAsF₆ (lithiumhexafluoro arsenate), LiCF₃SO₃ (lithium trifluoromethane sulfonate), andLiClO₄ (lithium perchlorate). Additional examples of suitable ionconducting layers include silicates, silicon oxides, tungsten oxides,tantalum oxides, niobium oxides, and borates. The silicon oxides includesilicon-aluminum-oxide. These materials may be doped with differentdopants, including lithium. Lithium doped silicon oxides include lithiumsilicon-aluminum-oxide. In some embodiments, the ion conducting layercomprises a silicate-based structure. In other embodiments, suitable ionconductors particularly adapted for lithium ion transport include, butare not limited to, lithium silicate, lithium aluminum silicate, lithiumaluminum borate, lithium aluminum fluoride, lithium borate, lithiumnitride, lithium zirconium silicate, lithium niobate, lithiumborosilicate, lithium phosphosilicate, and other such lithium-basedceramic materials, silicas, or silicon oxides, including lithiumsilicon-oxide.

The thickness of the ion conducting layer 10 will vary depending on thematerial. In some embodiments using an inorganic ion conductor the ionconducting layer 10 is about 250 nm to 1 nm thick, preferably about 50nm to 5 nm thick. In some embodiments using an organic ion conductor,the ion conducting layer is about 100000 nm to 1000 nm thick or about25000 nm to 10000 nm thick. The thickness of the ion conducting layer isalso substantially uniform. In one embodiment, a substantially uniformion conducting layer varies by not more than about +/−10% in each of theaforementioned thickness ranges. In another embodiment, a substantiallyuniform ion conducting layer varies by not more than about +/−5% in eachof the aforementioned thickness ranges. In another embodiment, asubstantially uniform ion conducting layer varies by not more than about+/−3% in each of the aforementioned thickness ranges.

Referring again to FIG. 1, substrates 24 and 25 have flat surfaces. Thatis, they have a surface coincides with the tangential plane in eachpoint. Although substrates with flat surfaces are typically employed forelectrochromic architectural windows and many other electrochromicdevices, it is contemplated that the multi-layer devices of the presentinvention may have a single or even a doubly curved surface. Stateddifferently, it is contemplated that each of the layers of stack 28 havea corresponding radius of curvature. See, for example, U.S. Pat. No.7,808,692 which is incorporated herein by reference in its entirety withrespect to the definition of single and doubly curved surfaces andmethods for the preparation thereof.

FIG. 17 depicts a cross-sectional structural diagram of anelectrochromic device according to a second embodiment of the presentinvention. Moving outward from the center, electrochromic device 1comprises electrochromic electrode layer 20. On either side ofelectrochromic electrode layer 20, in succession, are first and secondcurrent modulating structures 30, 31, first and second electricallyconductive layers 22, 23 and outer substrates 24, 25, respectively.Elements 22, 20, and 23 are collectively referred to as anelectrochromic stack 28. At least one of first and second electricallyconductive layers 22, 23 has a non-uniform sheet resistance as describedherein and at least one of first and second current modulatingstructures 30, 31 has a non-uniform cross-layer resistance as describedherein. Electrically conductive layer 22 is in electrical contact with avoltage source via bus bar 26 and electrically conductive layer 23 is inelectrical contact with a voltage source via bus bar 27 whereby thetransmittance of electrochromic device 20 may be changed by applying avoltage pulse to electrically conductive layers 22, 23. The pulse causesa cathodic compound in electrochromic electrode layer 20 to undergo areversible chemical reduction and an anodic compound in electrochromicelectrode layer 20 to undergo a reversible chemical oxidation. Eitherthe cathodic or anodic compound will demonstrate electrochromic behaviorsuch that electrochromic electrode layer 20 becomes less transmissive ormore transmissive after the pulse; in one embodiment, electrochromicdevice 1 has relatively greater transmittance before the voltage pulseand lesser transmittance after the voltage pulse or vice versa.

FIG. 18 depicts a cross-sectional structural diagram of anelectrochromic device according to a third embodiment of the presentinvention. Moving outward from the center, electrochromic device 1comprises ion conductor layer 10. Electrochromic electrode layer 20 ison one side of and in contact with a first surface of ion conductorlayer 10. First electrically conductive layer 22 is on one side ofelectrochromic layer 20 and second electrically conductive layer 23 ison a second, opposing side of ion conductor layer 10. First currentmodulating structure 30 is between electrochromic electrode layer 20 andelectrically conductive layer 22 and second current modulating structure31 is between ion conductor layer 10 and second electrically conductivelayer 23. At least one of first and second electrically conductivelayers 22, 23 has a non-uniform sheet resistance as described herein andat least one of first and second current modulating structures 30, 31has a non-uniform cross-layer resistance as described herein. In oneembodiment, one of electrically conductive layers 22, 23 contains apatterned conductive sublayer and has a non-uniform sheet resistance asa function of position and the other has a uniform sheet resistance as afunction of position. By way of further example, in another embodimentone of first and second electrically conductive layers 22, 23 contains apatterned conductive sublayer and has a non-uniform sheet resistance asa function of position and the other is a non-patterned layer having anon-uniform sheet resistance as a function of position. By way offurther example, in another embodiment first and second electricallyconductive layers 22, 23 each have a non-uniform sheet resistance as afunction of position. The first and second electrically conductivelayers 22, 23 are arranged against outer substrates 24, 25. Elements 10,20, 22 and 23 are collectively referred to as electrochromic stack 28.Electrically conductive layer 22 is in electrical contact with a voltagesource (not shown) via bus bar 26 and electrically conductive layer 23is in electrical contact with a voltage source (not shown) via bus bar27 whereby the transmittance of electrochromic layer 20 may be changedby applying a voltage pulse to electrically conductive layers 22, 23.Ion conductor layer 10 comprises a species that is capable of reversiblyoxidizing or reducing upon the insertion or withdrawal of electrons orions and this species may also be electrochromically active. The voltagepulse causes electrons and ions to move between first electrode layer 20and ion conducting layer 10 and, as a result, electrochromic materialsin the electrode layer 20 changes color, thereby making electrochromicdevice 1 less transmissive or more transmissive. In one embodiment,electrochromic device 1 has relatively greater transmittance before thevoltage pulse and relatively lesser transmittance after the voltagepulse or vice versa.

Referring again to FIGS. 1, 17, and 18 at least one of first and secondcurrent modulating structures 30,31 is also preferably transparent inorder to reveal the electrochromic properties of the stack 28 to thesurroundings. In one embodiment, first current modulating structure 30and first electrically conductive layer 22 are transparent. In anotherembodiment, second current modulating structure 31 and secondelectrically conductive layer 23 are transparent. In another embodiment,first and second current modulating structures 30, 31 and first andsecond electrically conductive layers 22, 23 are each transparent.

In general, the composition and sheet resistance profiles for first andsecond electrically conductive layers 22, 23 are as previously describedin connection with FIG. 1. Electrochromic electrode layers 20 may, forexample, contain an electrochromic material, either as a solid film ordispersed in an electrolyte, the electrochromic material being selectedfrom among inorganic metal oxides such as tungsten trioxide (WO₃),nickel oxide (NiO) and titanium dioxide (TiO₂), and organicelectrochromic materials including bipyridinium salt (viologen)derivatives, N,N′-di(p-cyanophenyl) 4,4′-bipyridilium (CPQ), quinonederivatives such as anthraquinone and azine derivatives such asphenothiazine.

In operation, to switch an electrochromic device of the presentinvention from a first to a second optical state having differingtransmissivities, i.e., from a state of relatively greatertransmissivity to a state of lesser transmissivity or vice versa, avoltage pulse is applied to the electrical contacts/bus bars on thedevice. Once switched, the second optical state will persist for sometime after the voltage pulse has ended and even in the absence of anyapplied voltage; for example, the second optical state will persist forat least 1 second after the voltage pulse has ended and even in theabsence of any applied voltage. By way of further example, the secondoptical state may persist for at least 5 seconds after the voltage pulsehas ended and even in the absence of any applied voltage. By way offurther example, the second optical state may persist for at least 1minute after the voltage pulse has ended and even in the absence of anyapplied voltage. By way of further example, the second optical state maypersist for at least 1 hour after the voltage pulse has ended and evenin the absence of any applied voltage. The device may then be returnedfrom the second optical state to the first optical state by reversingthe polarity and applying a second voltage pulse and, upon beingswitched back, the first optical state will persist for some time afterthe second pulse has ended even in the absence of any applied voltage;for example, the first optical state will persist for at least 1 secondafter the voltage pulse has ended and even in the absence of any appliedvoltage. By way of further example, the first optical state may persistfor at least 1 minute after the voltage pulse has ended and even in theabsence of any applied voltage. By way of further example, the firstoptical state may persist for at least 1 hour after the voltage pulsehas ended and even in the absence of any applied voltage. This processof reversibly switching from a first persistent to a second persistentoptical state, and then back again, can be repeated many times andpractically indefinitely.

In some embodiments the waveform of the voltage pulse may be designed sothat the local voltage across the electrochromic stack never exceeds apre-determined level; this may be preferred, for example, in certainelectrochromic devices where excessive voltage across the electrochromicstack can damage the device and/or induce undesirable changes to theelectrochromic materials.

Advantageously, the non-uniform sheet resistance of the first and/orsecond electrically conductive layers of the multi-layer devices of thepresent invention may permit greater tolerances with respect to themagnitude and/or duration of the voltage pulse. As a result, the localvoltage across the electrochromic stack may be significantly less thanthe voltage applied across the entire device because of the voltage dropin the electrically conductive layer(s). For example, in one embodiment,the applied potential across the electrochromic stack has a magnitude ofat least 2 Volts. By way of further example, the voltage pulse may havea magnitude of at least 3 Volts. By way of further example, the voltagepulse may have a magnitude of at least 4 Volts. By way of furtherexample, the voltage pulse may have a magnitude of at least 5 Volts. Byway of further example, the voltage pulse may have a magnitude of atleast 6 Volts. By way of further example, the voltage pulse may have amagnitude of at least 7 Volts. By way of further example, the voltagepulse may have a magnitude of at least 8 Volts. By way of furtherexample, the voltage pulse may have a magnitude of at least 9 Volts. Byway of further example, the voltage pulse may have a magnitude of atleast 10 Volts. By way of further example, the voltage pulse may have amagnitude of at least 11 Volts. By way of further example, the voltagepulse may have a magnitude of at least 12 Volts. By way of furtherexample, the voltage pulse may have a magnitude of at least 13 Volts. Byway of further example, the voltage pulse may have a magnitude of atleast 14 Volts. By way of further example, the voltage pulse may have amagnitude of at least 15 Volts. By way of further example, the voltagepulse may have a magnitude of at least 16 Volts. By way of furtherexample, the voltage pulse may have a magnitude of at least 18 Volts. Byway of further example, the voltage pulse may have a magnitude of atleast 20 Volts. By way of further example, the voltage pulse may have amagnitude of at least 22 Volts. By way of further example, the voltagepulse may have a magnitude of at least 24 Volts. In general, suchpotentials may be applied for a relatively long period of time. Forexample, a potential having a magnitude of any of such values may beapplied for a period of at least 1 seconds. By way of further example, apotential having a magnitude of any of such values may be applied for aperiod of at least 10 seconds. By way of further example, a potentialhaving a magnitude of any of such values may be applied for a period ofat least 20 seconds. By way of further example, a potential having amagnitude of any of such values may be applied for a period of at least40 seconds.

To illustrate for one specific exemplary embodiment, a voltage pulse of16 volts may be applied across an electrochromic stack incorporating twoTCO electrically conductive layers having non-uniform sheet resistanceand a bus bar located at opposite perimeter edges of the entire device.The voltage pulse rises quick to allow the local voltage drop across thelayers to quickly ramp to 1.0 volts and maintain that voltage until thedevice switching approaches completeness at which point the devicelayers begin to charge up and the current drops. Because of the gradientand sheet resistance in the electrically conductive layers the voltagedrop across the device is constant across the device and in addition,there is a voltage drop across each of the electrically conductivelayers of the device. The voltage drops through the non-uniformresistivity electrically conductive layers enables a voltagesignificantly larger than the maximum operating voltage of the devicestack to be applied across the entire assembly and maintain a localvoltage across the device stack below a desired value. As the devicecharging takes place, the applied voltage is dropped to keep the localvoltage across the device layers at 1.0 volts. The voltage pulse willdrop to a steady state value close to 1 volt if it is desired to keep asteady state 1.0 volts across the local device thickness oralternatively the voltage pulse will drop to zero volts if it is desiredto keep no voltage across the local device thickness in steady state.

To change the optical state of a multilayer device to an intermediatestate, a voltage pulse is applied to the electrical contacts/bus bars onthe device. This shape of this voltage pulse would typically be devicespecific and depend on the intermediate state desired. The intermediatestate can be defined in terms of a total charge moved, charge state ofdevice, or an optical measurement of the device. By using non-uniformelectron conductor layers to apply uniform local voltages across thedevice layers this provides a unique advantage for rapid large areaintermediate state control using optical state feedback since a localoptical measurement of the device state near the edge will berepresentative of the entire device at all times (no iris effect). Alsoby using non-uniform electron conductor layers to apply uniform localvoltages across the device layers this provides a unique advantage forrapid large area intermediate state control using voltage feedback sincethe voltage state at the bus bars will be representative of the entiredevice rather than an average across a non-uniformly colored device(again no iris effect). In a specific example, a voltage pulse of 32volts is applied across an electrochromic device incorporating twogradient TCO layers and a bus bar located at opposite perimeter edges ofthe entire device. The voltage pulse rises quick to allow the localvoltage drop across the layers to quickly ramp to 1.0 volts and maintainthat voltage until the device reaches a desired optical state measuredwith an appropriate optical sensor at which point the voltage pulsequickly ramps down to zero or to a desired steady state voltage.

One further advantage of the non-uniform resistance electrochromicdevices proposed herein, whether those comprising electricallyconductive layers with non-uniform sheet resistance and/or thosecomprising current modulating structures with non-uniform cross-layerresistance is that the control scheme used to drive and/or switch suchnon-uniform resistance electrochromic devices can be greatly simplified.For example, the control scheme may comprise a current driven mode wherea predetermined current is input to the electrochromic device for apredetermined time based on the charge capacity of the electrochromicdevice, the desired switching speed, and/or the target end state for theelectrochromic device. For non-uniform resistance electrochromicdevices, the non-uniform resistance thereof can make the voltage dropacross the device substantially constant, such that the optical state ofsuch non-uniform resistance electrochromic devices can be switcheduniformly across their entire area if desired. Accordingly, because ofsuch switching uniformity, the optical state of the non-uniformresistance electrochromic device can be controlled, predicted, and/orextrapolated with great precision across the entire area of theelectrochromic device by implementing simple current driving schemes,such as via a constant current voltage driven mode.

For instance, a non-uniform resistance electrochromic device maycomprise a charge capacity requiring a charge density or total chargeQ_(TOT) to fully switch optical states between a bleached state and anopaque or colored state. In some embodiments, the non-uniform resistanceelectrochromic device may comprise or be similar to one or more of thenon-uniform resistance devices shown or discussed with respect to thefigures, description, or embodiments disclosed herein. To switch thenon-uniformresistance electrochromic device to a target optical state, atarget charge Q_(TGT) for the non-uniform resistance electrochromicdevice can be calculated such that the ratio between target chargeQ_(TGT) and total charge Q_(TOT) reflects the target optical state. Forinstance, in one example, Q_(TGT) can be selected to be substantiallyequal to Q_(TOT) for establishing a maximum opacity or minimallybleached optical state, and/or Q_(TGT) can be selected to be at orapproximately zero for establishing a minimal opacity or maximum bleachoptical state. In a different example, Q_(TGT) can be selected to besubstantially equal to Q_(TOT) for establishing a minimum opacity ormaximum bleached optical state, and/or QTGT can be selected to be at orapproximately zero for establishing a maximum opacity or minimal bleachoptical state.

To switch the non-uniform resistance electrochromic device to the targetoptical state within a target switching time T_(TGT), a drive currentI_(DRV) could be calculated (I_(DRV)=Q_(TGT)/T_(TGT)) and fed to thenon-uniform resistance electrochromic device to satisfy the desiredswitching and time requirements, with the expectation that thenon-uniform resistance electrochromic device will uniformly achieve thetarget optical state at the end of target time T_(TGT) and throughoutthe entire area of the non-uniform resistance electrochromic device. Insome examples, drive current I_(DRV) can simply be a constant current.If a full switch between bleached and opaque states is not desired, thedrive current I_(DRV) can be adjusted accordingly. For example, toachieve a 50% switch between the bleached and opaque optical states,target charge Q_(TGT) can be set to 50% of total charge Q_(TOT).Accordingly, to satisfy Q_(TGT)=(I_(DRV))(T_(TGT)), either drive currentI_(DRv) can be decreased by 50%, or time T can be decreased by 50%, withthe expectation that the non-uniform resistance electrochromic devicewill uniformly achieve a 50% opacity optical state at the end of time Tand throughout the entire area of the non-uniform resistanceelectrochromic device. Such simplicity and predictability contrasts withprior art electrochromic devices, avoiding the need to worry about iriseffect and the unpredictability it introduces as to the optical state ofdifferent portions of the electrochromic device, and avoiding the needfor complicated driving schemes attempting to compensate for theswitching non-uniformity of such prior art electrochromic devices.

To test the simplified control scheme described above, an experimentalsetup of the above simplified current driven mode scheme was implementedfor a test non-uniform resistance electronic device. The test device hadglass substrates that were 9 cm wide by 70 cm long. The electricallyconductive layers on these substrates were designed with opposingresistivity gradients for uniform switching along the entire length ofthe test device, such as described above with respect to device 1 ofFIG. 1 and/or the circuit model of FIG. 19. The test device had a firstbusbar coupled a first electrically conductive layer of the test device,and a second busbar coupled to a second electrically conductive layer ofthe test device, where the busbars were located at opposite ends of thelength of the test device. The busbars were coupled to power source inthe form of a Keithley 2400 sourcemeter from Keithley Instruments, Inc.of Cleveland, Ohio, which was configured to output drive current I_(DRV)to the busbars. A data acquisition (DAQ) unit was also coupled to thetest device to measure voltage at the longitudinal center andlongitudinal edges of the anode and cathode electrically conductivelayers electrically conductive layers to measure the difference betweenanode and cathode voltages at such locations. The charge capacity of thetest device was of 5 Coulombs, such that a charge density Q_(TOT) of 5Coulombs would be necessary to fully switch the optical state of thetest device between bleached and opaque states. Accordingly, for adesired target switching time T_(TGT) of 250 seconds to go fromcompletely bleached to completely opaque, a drive current I_(DRV) of 20mA would be needed from the power source to establish the needed currentdriven mode for the test device. The power source was thus configured todeliver the I_(DRV) of 20 mA as a constant current to the busbars of thetest device and, at the end of the switching time T of 250 seconds, thetest device had fully and uniformly switched its optical state to fullyopaque in accordance with the predicted calculation. In addition, theDAQ confirmed that the local device voltages at the longitudinal edgesand center of the test device were similar to each other.

A similar test was performed for switching the test device to anintermediate optical state. For example, to switch the test device to atarget optical state of 50% opacity, Q_(TGT) was calculated to be 2.5Coulombs (50% of Q_(TOT)). To achieve 2.5 Coulombs=Q_(TGT)=(I_(DRV))(T),I_(DRV) was reduced by 50% to 10 mA while leaving target time T_(TGT) at250 seconds. As another test, to achieve 2.5 Coulombs=Q_(TGT), T_(TGT)was reduced to 125 seconds while leaving I_(DRV) at 20 mA. Othersuitable combinations of I_(DRV) and T_(TGT) can also be combined toachieve the desired target charge of Q_(TGT) in the same or otherimplementations.

As part of the experimental setups above, local voltages were monitoredat different locations of the test device was to ensure that such localvoltages would remain within a safe operating window to prevent damageto the test device. For example, if the drive current were tooaggressive in an attempt to switch the optical state of the device tooquickly, an overdrive situation may ensue where local voltage wouldexceed the operational limits at certain locations of the electrochromicdevice. As an example, prior art uniform resistivity electrochromicdevices tend to experience voltage overdrive conditions at the edgesthereof, such as near the busbars, while the center and other locationsaway from the edges remain within a safe operating voltage window.Accordingly, for uniform resistivity electrochromic devices, voltageoverdrive is best monitored towards the edges and/or near the busbars ofsuch devices. In contrast, for non-uniform resistance electrochromicdevices, voltage overdrive may be monitored elsewhere, such as at thecenter of the device and/or at a point of least resistance between thecathode and anode of the device. In any event, the simplified controlscheme for gradient resistance electrochromic devices described abovemay be configured with a safety feature for switching from the describedcurrent driven mode to a voltage driven mode when approaching a voltageoverdrive condition, where the voltage driven mode decreases the drivecurrent I_(DRV) such as not to exceed a maximum voltage (Vmax) orminimum voltage (Vmin) limit at the device location being monitored.

Having described the invention in detail, it will be apparent thatmodifications and variations are possible without departing the scope ofthe invention defined in the appended claims. Furthermore, it should beappreciated that all examples in the present disclosure are provided asnon-limiting examples.

EXAMPLES Example 1 Patterned Current Modulating Layer

A current modulating layer was fabricated on the surface of anelectrically conductive layer of Fluorine doped Tin Oxide (FTO) toproduce a parabolic cross-layer resistance profile in a directionparallel to one of the sample sides.

The substrate material used for this example was 90 mm by 137 mmPilkington TEC250 (FTO coated soda lime glass) having a sheet resistanceof 250 Ω/□. The substrate was first cleaned using a 1% solution ofAlcanox in water, rinsed with de-ionized water and isopropyl alcohol,then sputter-coated with a 50 nm, uniform film of insulating SiO₂. Thesubstrate was then coated with a polymeric positive photoresist, anddeveloped under UV using a photomask purchased from Photo Sciences, Inc.The pattern developed is illustrated schematically on FIG. 4D. The blackareas represent areas where the photoresist was developed and removedfrom the silica coating. The boxes were arranged according to a 1 mmpitch array. The area of the boxes increased parabolically as a functionof position in the 137 mm direction, from 10 um² on both edge to 1 mm²in the center. A physical plasma etch was used in order to remove thesilica coating off the FTO in the developed boxes. After the plasmaetch, the photoresist was stripped off and the sample cleaned a secondtime before being coated with TiO₂.

The TiO₂ was coated using a sol-gel process. The sol-gel precursor wasprepared in 1-Butanol with titanium isopropoxide and acetylacetone, bothhaving a concentration in solution of 0.4 mol/L. After spin-coating thesolution at 1500 rpm for 1 minute, the substrate was calcined to 400Cfor 1 hour. The thickness of the TiO₂ was measured using a dektakprofilometer to be around 80 nm. The resulting composite is a currentmodulating layer where electrons must flow through the apertures in theSiO₂ coating (which vary in size with respect to position) and throughthe TiO₂ coating before reaching the surface of the composite stack.

Example 2 Patterned Composite Electrically Conductive Layer of VaryingSheet Resistance

A patterned composite electrically conductive layer was fabricated toproduce a linear sheet resistance gradient.

The substrate material used for this example was 105 mm by 11 5 mmPilkington TEC15 (Fluorine doped tin oxide (FTO) coated soda lime glass)having a sheet resistance of 15 Ω/□. The substrate was first patternedusing a 1064 nm YVO4 laser marking tool, to remove FTO off the surfaceof the glass in desired areas. The type of pattern used is illustratedschematically in FIG. 20. The areas colored in black represent regionswhere the TCO has been removed from the surface of the glass. In thepresent example, the deleted areas are square boxes, arranged in a 1 mmpitch array, where the size of the deleted boxes increase in thedirection parallel to the 115 mm side (the direction of the desiredgradient), and remain the same in the direction normal to the 115 mmside. The boxes were varied in size from 0.184 mm2 to 0.933 mm2 as afunction of position along the 11.5 mm side, according to a non-linearfunction. This function was determined using electrical modeling of thecomposite, and fits the following equation:y=5E-10x⁵-2E-07x⁴+2E-05x³-0.0013x²+0.0439x+0.1989, where y is the areaof a box (in mm2) and x is the location (in mm) on the substrate, in the115 mm direction.

The patterned FTO was then sputter-coated with 10 nm of Indium Tin Oxide(ITO), having a bulk conductivity of around 4.5E-4 Ω·cm. The resultingcomposite of FTO and ITO was characterized using a custom voltagemapping tool to measure the resistance of the composite as a function ofposition. The sheet resistance varied from 14.4 Ω/□ to 180 Ω/□.

What is claimed is:
 1. An electrochromic device comprising a firstsubstrate, a first electrically conductive layer, a first currentmodulating structure, a first electrode layer, a second electricallyconductive layer and a second substrate, the electrically conductivelayer and the first current modulating structure each covering at least0.01 m² of the surface of the first substrate, the first currentmodulating structure being between the first electrically conductivelayer and the first electrode layer, the first current modulatingstructure comprising a material having a resistivity of at least10⁴Ω·cm, the first electrically conductive layer having a sheetresistance, R_(s), to the flow of electrical current through the firstelectrically conductive layer that varies as a function of position inthe first electrically conductive layer, wherein an average sheetresistance in a first region of the first electrically conductive layercircumscribed by a first convex polygon to the average sheet resistancein a second region of the first electrically conductive layercircumscribed by a second convex polygon is at least 2, the first andsecond regions circumscribed by the first and second convex polygons,respectively, each comprising at least 25% of the surface area of thefirst electrically conductive layer.
 2. The electrochromic device ofclaim 1, further comprising first and second busbars respectivelycoupled to the first and second electrically conductive layers wherein(i) the first and second busbars are configured to receive a drivecurrent I_(DRV) to enable a current driven mode for switching theelectrochromic device to a target optical state with respect to aminimum optical state and a maximum optical state thereof; (ii) theelectrochromic device comprises a total charge capacity having a totalcharge Q_(TOT); (iii) the target optical state is attainable by chargingthe electrochromic device to a target charge Q_(TGT) via the drivecurrent I_(DRV), the target charge Q_(TGT) comprises a percentage of thetotal charge Q_(TOT) corresponding to a percentage of the target opticalstate relative to the maximum optical state; and (iv) the target opticalstate is predictably attainable for substantially all of a totaloptically switchable area of the electrochromic device, and within atarget time T_(TGT), by adjustment of the drive current I_(DRV) suchthat the product of the target time T_(TGT) and the drive currentI_(DRV) substantially equals the target charge Q_(TGT).
 3. Theelectrochromic device of claim 2, wherein the optically switchable areaof the electrochromic device is transitionable to the target opticalstate once the drive current I_(DRv) is adjusted to a constant currentvalue corresponding to the target time T_(TGT).
 4. The electrochromicdevice of 1 wherein (i) the ratio of the average sheet resistance in afirst region of the first electrically conductive layer circumscribed bya first convex polygon to the average sheet resistance in a secondregion of the first electrically conductive layer circumscribed by asecond convex polygon is at least 2, the first and second regions of thefirst electrically conductive layer each comprising at least 25% of thesurface area of the first electrically conductive layer and (ii) theratio of the average sheet resistance in a first region of the secondelectrically conductive layer circumscribed by a first convex polygon tothe average sheet resistance in a second region of the secondelectrically conductive layer circumscribed by a second convex polygonis at least 2, the first and second regions of the second electricallyconductive layer each comprising at least 25% of the surface area of thesecond electrically conductive layer.
 5. The electrochromic device ofclaim 1 wherein the first electrically conductive layer has a spatiallyvarying sheet resistance, R_(s), that varies as a function of positionin the first electrically conductive layer, a contour map of the sheetresistance, R_(s), as a function of position within the firstelectrically conductive layer contains a set of isoresistance lines anda set of resistance gradient lines normal to the isoresistance lines,and the sheet resistance along a gradient line in the set generallyincreases, generally decreases, generally increases until it reaches amaximum and then generally decreases, or generally decreases until itreaches a minimum and then generally increases.
 6. The electrochromicdevice of claim 5 wherein the second electrically conductive layer has aspatially varying sheet resistance, R_(s), that varies as a function ofposition in the second electrically conductive layer, a contour map ofthe sheet resistance, R_(s), as a function of position within the secondelectrically conductive layer contains a set of isoresistance lines anda set of resistance gradient lines normal to the isoresistance lines,and the sheet resistance along a gradient line in the set generallyincreases, generally decreases, generally increases until it reaches amaximum and then generally decreases, or generally decreases until itreaches a minimum and then generally increases.
 7. The electrochromicdevice of claim 1 wherein the second substrate and the secondelectrically conductive layer are transparent to electromagneticradiation having a wavelength in the range of infrared to ultraviolet.8. The electrochromic device of claim 1 wherein the electrochromicdevice comprises, in succession, the first substrate, the firstelectrically conductive layer, the first current modulating structure,the first electrode layer, an ion conducting layer, a second electrodelayer, the second electrically conductive layer and the secondsubstrate.
 9. The electrochromic device of claim 1 wherein the firstelectrically conductive layer comprises a first material and a secondmaterial, the first material being a transparent conductive oxide andthe second material having a resistivity that is greater than theresistivity of the first material by a factor of at least 10².
 10. Theelectrochromic device of claim 1 wherein the current modulatingstructure comprises resistive material.
 11. The electrochromic device ofclaim 1 wherein the current modulating structure comprises insulatingmaterial.
 12. A process for the preparation of a multi-layer devicecomprising forming a multi-layer layer structure comprising anelectrochromic layer between and in electrical contact with a first anda second electrically conductive layer, and a first current modulatingstructure between the first electrically conductive layer and theelectrochromic layer, the first current modulating structure comprisinga material having a resistivity of at least 10⁴ Ω·cm, the first and/orthe second electrically conductive layer having a spatially varyingsheet resistance, R_(s), to the flow of electrical current through thefirst and/or the second electrically conductive layer that varies as afunction of position in the first and/or the second electricallyconductive layer, respectively, wherein the ratio of the average sheetresistance in a first region of the first electrically conductive layercircumscribed by a first convex polygon to the average sheet resistancein a second region of the first electrically conductive layercircumscribed by a second convex polygon is at least 2, the first andsecond regions circumscribed by the first and second convex polygons,respectively, each comprising at least 25% of the surface area of thefirst electrically conductive layer.
 13. The process of claim 12 whereinthe first electrically conductive layer has a spatially varying sheetresistance, R_(s), that varies as a function of position in the firstelectrically conductive layer, a contour map of the sheet resistance,R_(s), as a function of position within the first electricallyconductive layer contains a set of isoresistance lines and a set ofresistance gradient lines normal to the isoresistance lines, and thesheet resistance along a gradient line in the set generally increases,generally decreases, generally increases until it reaches a maximum andthen generally decreases, or generally decreases until it reaches aminimum and then generally increases.
 14. The process of claim 12wherein the first electrically conductive layer comprises a firstmaterial and a second material, the first material being a transparentconductive oxide and the second material having a resistivity that isgreater than the resistivity of the first material by a factor of atleast 10².
 15. The process of claim 12 wherein the current modulatingstructure comprises resistive material.
 16. The process of claim 12wherein the current modulating structure comprises insulating material.